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Why Transitivity Violations Can Be Rational

Unknown Lamer posted about 7 months ago | from the error-axiom-broken dept.

Science 169

ananyo writes "Organisms, including humans, are often assumed to be hard-wired by evolution to try to make optimal decisions, to the best of their knowledge. Ranking choices consistently — for example, in selecting food sources — would seem to be one aspect of such rationality. If A is preferred over B, and B over C, then surely A should be selected when the options are just A and C? This seemingly logical ordering of preferences is called transitivity. Furthermore, if A is preferred when both B and C are available, then A should 'rationally' remain the first choice when only A and B are at hand ... But sometimes animals do not display such logic. For example, honeybees and gray jays have been seen to violate the Independence of Irrational Alternatives, and so have hummingbirds ... Researchers have now used a theoretical model to show that, in fact, violations of transitivity can sometimes be the best choice (original paper) for the given situation, and therefore rational. The key is that the various choices might appear or disappear in the future. Then the decision becomes more complicated than a simple, fixed ranking of preferences. So while these choices look irrational, they aren't necessarily."

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Most likely exists to prevent over-grazing.. (0)

Anonymous Coward | about 7 months ago | (#45965193)

... any given food source.

Re:Most likely exists to prevent over-grazing.. (4, Insightful)

happy_place (632005) | about 7 months ago | (#45965305)

It might also have to do with competition. If there's little competition for my preferred food source, I will eat it last, knowing it will last longer. My wife hates dark chocolate, but I prefer it, so if there's a bag of chocolate bars and dark chocolate, I'll dig into the milk chocolate first, knowing that my wife will actively consume those as well, then when they're gone, I still have the dark chocolate to enjoy afterwards, while she's without.

Re:Most likely exists to prevent over-grazing.. (-1, Troll)

Anonymous Coward | about 7 months ago | (#45965325)

Your wife sounds fat...

Re:Most likely exists to prevent over-grazing.. (5, Insightful)

sixoh1 (996418) | about 7 months ago | (#45965447)

If your wife reads Slashdot this little game could end quite badly... never get between a woman and her chocolate!

Re:Most likely exists to prevent over-grazing.. (3, Interesting)

turning in circles (2882659) | about 7 months ago | (#45965489)

Yes, this is the point of the article. Your ability to look into the future may make you change your current preferences. You know the dark chocolate won't run out, so to maximize your chocolate intake, you eat the milk chocolate first. If your wife were visiting her sister for an extended period of time, you'd probably eat the dark chocolate first, because you like it better.

This is, of course, not nice (wife "I bought the dark for you and the milk for me"), but is probably rational.

Re:Most likely exists to prevent over-grazing.. (2)

CanHasDIY (1672858) | about 7 months ago | (#45965553)

My wife hates dark chocolate, but I prefer it, so if there's a bag of chocolate bars and dark chocolate, I'll dig into the milk chocolate first, knowing that my wife will actively consume those as well, then when they're gone, I still have the dark chocolate to enjoy afterwards, while she's without.

So, you purposefully over indulge, pigging out on the thing your wife likes to intentionally deprive here, meanwhile stashing back stuff you know she won't eat?

I do not expect your marriage is going to last all that long...

Re:Most likely exists to prevent over-grazing.. (4, Insightful)

EmagGeek (574360) | about 7 months ago | (#45965763)

You obviously know nothing about women.

My wife loves chocolate as well, but hates to eat it because she likes being skinny more than she likes eating chocolate (and if you ask any woman, the two are mutually exclusive). So, if I have chocolate in the house, I must compete with her and ensure that I eat most of it, otherwise she gets upset.

Re:Most likely exists to prevent over-grazing.. (0, Troll)

CanHasDIY (1672858) | about 7 months ago | (#45965983)

You obviously know nothing about women.

My wife loves chocolate as well, but hates to eat it because she likes being skinny more than she likes eating chocolate (and if you ask any woman, the two are mutually exclusive).

Right: You're the one perpetuating misogynistic stereotypes, but I'm the guy who knows nothing about women...

Re:Most likely exists to prevent over-grazing.. (2)

The Mighty Buzzard (878441) | about 7 months ago | (#45966167)

Stereotypes generally have a damned good reason to be stereotypes. Getting called misogynistic or not, if it's true of a significant enough subsample of the population, it can and should be used.

Re:Most likely exists to prevent over-grazing.. (0)

CanHasDIY (1672858) | about 7 months ago | (#45966339)

Stereotypes generally have a damned good reason to be stereotypes. Getting called misogynistic or not, if it's true of a significant enough subsample of the population, it can and should be used.

So, then, when you see a black person carrying a watermelon you assume they stole it? I guess you try to hire as many Asians for mathematical jobs as you can, right? And lordy lord, don't let none of those Native Americans near the firewater, since they stereotypically can't help but become alcoholics.

Stereotypes generally exist because marginalizing someone with a derogatory label makes it easier to do fucked up things to them.

Re:Most likely exists to prevent over-grazing.. (3, Insightful)

Oligonicella (659917) | about 7 months ago | (#45966393)

You are the most knee-jerk racist hiding in a "liberal" sheep's coat that I've ever read comment here.

Re:Most likely exists to prevent over-grazing.. (0, Offtopic)

CanHasDIY (1672858) | about 7 months ago | (#45966799)

You are the most knee-jerk racist...

Why? I'm not the one saying that stereotypes are accurate.

... hiding in a "liberal" sheep's coat that I've ever read comment here.

That's cute, the whole "liberal sheep's coat" thing, whatever it's supposed to mean. I guess, for you, it's not possible for a person to, say, support social welfare as a fiscal conservative, or be pro-2nd Amendment and... uh...

OK, to be honest, outside of the aforementioned topics (and abortion) I really have zero clue as to what defines a person as a "liberal" or "conservative" in the political sense. I prefer to just be me, not affiliated with any party or group, and holding my own opinions instead of having them spoon fed to me. So when a self-defined "conservative" accuses me of being "liberal," or vice-versa, I normally just chalk it up to that person being ignorant of both the terms used and topic at hand.

Re:Most likely exists to prevent over-grazing.. (0)

Anonymous Coward | about 7 months ago | (#45966497)

Sorry, no. And this is a good thread for this. Stereotypes are a survival mechanism. Stereotypes are not like laws. Humans don't make them up. They exist for real in the world, and they are what has allowed humans (and all animal life, really) to survive.

Re:Most likely exists to prevent over-grazing.. (1)

kekx (2828765) | about 7 months ago | (#45966195)

C'mon that was obviously a joke... How cranky can one be?

Re:Most likely exists to prevent over-grazing.. (2)

CanHasDIY (1672858) | about 7 months ago | (#45966363)

C'mon that was obviously a joke... How cranky can one be?

You might be surprised - I once knew a lesbian femi-nazi who could, somehow, find offense in you hugging someone, assuming you have a penis.

Welcome to 'Murica, Land of the Cranks, Home of the Narcissistic.

Re:Most likely exists to prevent over-grazing.. (2)

Jeff Flanagan (2981883) | about 7 months ago | (#45966937)

Do you not realize that in saying things like "femi-nazi," you are one of the cranks you deride?

Re:Most likely exists to prevent over-grazing.. (1)

CanHasDIY (1672858) | about 7 months ago | (#45967177)

Do you not realize that "opinion != fact?"

Besides, I never disqualified any 'Murican from being a crank, present company included.

Re:Most likely exists to prevent over-grazing.. (1)

hawkfish (8978) | about 7 months ago | (#45966955)

You obviously know nothing about women.

My wife loves chocolate as well, but hates to eat it because she likes being skinny more than she likes eating chocolate (and if you ask any woman, the two are mutually exclusive).

Right: You're the one perpetuating misogynistic stereotypes, but I'm the guy who knows nothing about women...

...and you are the one who missed that the GP was making a statement of fact about one particular woman who they know well, not making a stereotypical generalisation. But since you bring it up, my wife has also said this to me pretty much verbatim...

Re:Most likely exists to prevent over-grazing.. (0, Offtopic)

CanHasDIY (1672858) | about 7 months ago | (#45967227)

You obviously know nothing about women.

My wife loves chocolate as well, but hates to eat it because she likes being skinny more than she likes eating chocolate (and if you ask any woman, the two are mutually exclusive).

Right: You're the one perpetuating misogynistic stereotypes, but I'm the guy who knows nothing about women...

...and you are the one who missed that the GP was making a statement of fact about one particular woman who they know well, not making a stereotypical generalisation.

So, the phrase, "and if you ask any woman..." doesn't imply generalization? Sure sounds that way to me.

But since you bring it up, my wife has also said this to me pretty much verbatim...

Oh, cool, so anecdotes have become the plural of evidence? Because I know a lot of women who would take offense to that, and since "a lot" is obviously more than 2, then by your 'logic' I am correct.

Re:Most likely exists to prevent over-grazing.. (1)

Ferrofluid (2979761) | about 7 months ago | (#45967215)

purposefully

Purposely. Purposefully means something else.

Re:Most likely exists to prevent over-grazing.. (5, Insightful)

ZahrGnosis (66741) | about 7 months ago | (#45965629)

One of my pet peeves with discussions on evolution is the assumption, in general, that any given trait or behavior evolved for a particular reason, or that any one concept such as "logical rationality" can explain the whole evolution of a single such trait. In fact this sounds more like intelligent design than evolution. It's an interesting exercise to track a trait through evolution, but there's a fine line between that and presupposing that every behavior must occur due to some underlying logic.

We're talking about behavior that evolved due to an absurd amount of chaos; how was it not obvious that a "decision becomes more complicated than a simple, fixed ranking of preferences"? And who gets to decide what's "rational"... from a basic evolutionary perspective, anything that has evolved to this point and is still alive and kicking is doing well; it's almost impossible to call any such evolution "irrational", so finding ways to prove it so is just silly. I mean, there's plenty of evolution that seems odd... flightless birds, blind species with eyes, animals that eat their young and their mates... but these species all survive and procreate and carry on from one generation to the next. Why does everything have to be nice and tidy... what's the obsession with "rational"? In fact, the behavior described in the article sounds more rational than the opposite... consider Pandas, who exist almost entirely on one food (bamboo)... these animals are very nearly extinct due to this behavior (some people assert that they would be if it weren't for human efforts to save them). Is that rational from an evolutionary perspective?

I'm sure I sound annoyed, but some times we try to oversimplify things way too much. happy_place is correct; competition could matter, and individual preference clearly exists all over the place... why does there have to be a rationalization? Is it an evolutionary benefit that happy_place likes dark chocolate while their wife hates it? More likely it's just a quirk of evolution, not a grand result of evolution having evolved precisely so that our species won't starve when cocoa is the last remaining food on the planet.

Let me put it this way... given whole of evolution, I would wager that for any categorization of traits that are well defined (such as "rational"), there exists at least one example that is both in and out of that category. SOMETHING has evolved irrationally, oddly, stupidly, and without purpose, due only to quirks of evolution that didn't really get in the way of a species survival, but didn't necessarily help it along either.

Re:Most likely exists to prevent over-grazing.. (1)

iMadeGhostzilla (1851560) | about 7 months ago | (#45966381)

Exactly! Those who insist on man-made "rational reasons" for evolution differ from those believing in Intelligent Design only in that they worship a different entity. What is rational, and what is even a "reason" -- a clearly defined arrow of consequence from what we chose to call A to what we chose to call B -- in an infinite chaos that we tried to map mentally? There's a great quote from some French philosopher along the lines of what you said, "logic excludes -- by definition -- nuances, and Truth resides exclusively in nuances."

Re:Most likely exists to prevent over-grazing.. (1)

Oligonicella (659917) | about 7 months ago | (#45966449)

Add to that, many of those "researchers" have little actual knowledge about the animals involved, only focusing on the traits that appeal to their line of investigation. This is most easily spotted when they cross genus - hell, cross Order - boundaries to make comparisons. Birds and insects do not share the same drives, for instance.

Re:Most likely exists to prevent over-grazing.. (0)

Anonymous Coward | about 7 months ago | (#45966907)

That's a fair point, but the experiments cited in the paper all focused on food gathering, and the experiments always weighed quantities against effort, e.g. putting one raisin near the front of a cardboard tube and two raisins near the back of a different tube, and seeing which tube a bird crawls into first. We aren't asking why birds prefer black raisins over golden raisins, or whether they prefer raisins over nuts. We're asking how much extra effort they're willing to put into getting a second raisin.

It's reasonable to expect evolution to select for the Big Three: sexual preference, predator avoidance, and efficient food gathering. If evolution doesn't select for efficient food gatherers, what does it select for?

Ranked preference voting (1)

goombah99 (560566) | about 7 months ago | (#45966285)

Your comment and and the article remind me of strategies employed in voting systems. Arrow famously put forth arrows axioms of fairness for selecting a voting system, one of those axioms was the irrelevance to alternatives when comparing two canadidates. that is, your preference for candidate A over candidate B should not change if candidate C runs or not. We also believe that preferences are transitive, and transitivity should mean you can rank your preferences in a set of candidates. The interesting thing he showed was there was no possible voting system that could satisfy all of the axioms for a group of people under all circumstances. However, there is one voting system does work under most non-pathological systems. And this is Condorcet voting also known as "majority rule, ranked preference.". IN this system everyone ranks the candidates then to tally you consider each possible pair of candidates and momentarily consider the outcome if none of the other candidates existed. If, as is nearly always the case, one candidate would beat all the other candidates in a pairwise battle this person is the winner. In rare cases where that's not true, special handling rules can be invoked.

What's amusing about this is that this nearly optimal ranked preference voting protocol is both simple and known. Yet most ranked preference voting is implemented as Instant Runnoff voting which is one of the worst possible ways to tabulate and frequently violates arrows axioms of fairness. The problem with Instant runoff voting is that it falls victim to the strategy you are using to get more of the chocolate for your self: strategically mis-ranking your preferences. Another problem with Instant run-off voting when there are three or more nearly equal strength candidates. It tends to pick wing parties over centrist parties--- which intuitively should tell you something is wrong. Here's and example of that:

suppose I have a left, center and Right candidates names L,C and R. you can imagine ranking after vote tablualtion might look like this:

R > C > L 35%
C > R > L 16%
C > L > R 15%
L > C > R 34%

Now who should win? Well if R had not run then C would have beat L in a landslide 66% to 34%. Likewise C beats R 65% to 34%. So clearly C is the person a majority will be happy with no matter who else is running. But what does instant Run-off voting do? Well it tabluates the first round of preferences: 35 to 32 to 34 for R:C:L and then since C has the lowest first round vote, C is removed. Then we move to the second round and there, without C in the race, R beats in the ratio 51 to 49%.

Which is nuts because 66 % of the voters prefer C to L!

So be sure to laugh at people who tell you they want instant run-off voting. sadly this is what is mainly being implemented.

irrational verus rational multi-objective logic (1)

goombah99 (560566) | about 7 months ago | (#45966421)

Oops, I deleted a key point from my comment. Arrows result shows that even if every individual has a transitive preference order, that a group does not always have a transitive preference order. in terms of Condorect voting this would mean that under rare cases one can have A > B, B > C and C>A, which is a non-tranistive cycle for the groups combined preferences.

Thus one way to explain non-trainsitive behaviour in individuals would be to postulate that internally individuals are groups! your left brain wants one thing and your right brain wants something else, and your penis might have yet another opinion on the subject. When you merger those individually transitive preferences you can get a non-transitive outcome that must be resolved by some ad hoc tie resolution protocol.

So the point is non]-transitive behaviour can emerge not simply as a devious stratgy about future choices but also simply when one has a mult-objective preference function to satisfy. Neither of these is irrational.

Re:irrational verus rational multi-objective logic (0)

Anonymous Coward | about 7 months ago | (#45967411)

I don't think people are good at ranking alternatives within a group. Better, and much simpler, to evaluate each alternative individually and decide if it an acceptable choice or not. In other words, approval voting, that is a simple approve (or by absence of an approval, not approving) a choice is much easier than creating an ordered ranking of all candidates. 3 candidates, like all of them or none? like only one? like two out of the three, then approve of the ones you can accept. Much easier than deciding which is better than the other especially if two are equally very bad, etc. Then add all the approvals, and the candidate with the most votes wins. N candidates, N possible yes votes. Better than the current system with N candidates, only one possible vote. No "wasted" votes if you can only vote for a third party candidate. You can approve of that candidate and a major party one if you want. Less voter apathy. More engagement. No problem choosing among the lesser of evils, etc. Approval voting = a simpler, easy to understand, and likely superior voting system.

Re:irrational verus rational multi-objective logic (1)

goombah99 (560566) | about 7 months ago | (#45967505)

Yes, I agree. Approval voting has much to be desired, especially it's simplicity of implementation and its assymtotic approach to rangevoting without all the complexity. I was discussing instant run-off voting and how transitivity violations arise so I did not bring this up.

Re:Most likely exists to prevent over-grazing.. (0)

Anonymous Coward | about 7 months ago | (#45966399)

It might also have to do with competition. If there's little competition for my preferred food source, I will eat it last, knowing it will last longer. My wife hates dark chocolate, but I prefer it, so if there's a bag of chocolate bars and dark chocolate, I'll dig into the milk chocolate first, knowing that my wife will actively consume those as well, then when they're gone, I still have the dark chocolate to enjoy afterwards, while she's without.

You prefer dark chocolate, but will eat the milk chocolate just to spite her? Holy shit, that's selfish. Do you love your wife?

Re:Most likely exists to prevent over-grazing.. (1)

godrik (1287354) | about 7 months ago | (#45966645)

What a jerk!

Re:Most likely exists to prevent over-grazing.. (1)

TheCarp (96830) | about 7 months ago | (#45965459)

Not just any given food source but... there is a base assumption in this simplified "logic" that any once choice is necessarily viable as an only option. What if no member of the set A, B, or C, provides all of the needed nutrients? Sure I can eat A preferencially, but, if I eat it to exclusion, that means that I live chronically with any deficits in what it provides.

Since its unlikely that any given organism can fully distinguish its own nutritional needs compared to a single food source, drawing from multiple food sources to get a blend of nutrient compositions is not a terrible strategy.

Re:Most likely exists to prevent over-grazing.. (1)

SQLGuru (980662) | about 7 months ago | (#45965853)

Rock, Paper, Scissors (Lizard, Spock). If you prefer Rock and all three options are available, you'll favor Rock. However, if you know that Paper has been eliminated as a choice, you'll pick Scissors because Scissors beat Rock. Of course, in this sort of set-up, I would guess that there wouldn't be a group bias towards any one resource (individual bias, but not a group bias).

Re:Most likely exists to prevent over-grazing.. (0)

Anonymous Coward | about 7 months ago | (#45966711)

Yea, that really worked out for the St. Matthew Island Reindeer.

Ranking choices consistently (0, Troll)

tomhath (637240) | about 7 months ago | (#45965195)

In other words, the scientists didn't understand the criteria for ranking the choices. Nothing to see here...

Re:Ranking choices consistently (3, Insightful)

MightyYar (622222) | about 7 months ago | (#45965349)

In fact it is the opposite - scientists previously didn't understand the criteria, and now they think that they do. It is progress in our understanding of the natural world.

Re:Ranking choices consistently (0)

Arkh89 (2870391) | about 7 months ago | (#45965415)

Yes, but this has nothing to do with a violation of transitivity... It is just that their model for food attractiveness which was wrong. If you correct the model, then you should get back transitivity (basic optimizations rule).

Re:Ranking choices consistently (1)

Anonymous Coward | about 7 months ago | (#45965579)

No, the corrected model would incorporate the reason for breaking transitivity. Transitivity would still be broken, we would just have an explanation for it.

Transitivity is broken in many ways. I once had a set of game spinners that proved this. Spinner A would on average beat Spinner B (stop on a higher value), Spinner B would on average beat Spinner C, but Spinner C would on average beat spinner A kind of a neat trick.

Re:Ranking choices consistently (0)

Anonymous Coward | about 7 months ago | (#45965639)

My bad, I forgot the most simple violation of transitivity. Rock beats Scissors; Scissors beats Paper; Therefore Rock must beat Paper. WRONG. Paper beats Rock.

Re:Ranking choices consistently (1)

Arkh89 (2870391) | about 7 months ago | (#45965949)

My point is more about the Mathematical objects rather than the thinking. Your last example does not matter as it is not an ordered set. Although, as I said in my first message, I think that they should not say that transitivity is broken but rather that the food attractiveness function can be changed by some events, thus reordering the elements in the set Foods. Or that Foods is not an ordered set and thus, no comparison operator can be applied.

Re:Ranking choices consistently (1)

tomhath (637240) | about 7 months ago | (#45966291)

I think that they should not say that transitivity is broken but rather that the food attractiveness function can be changed by some events

That's exactly my original point (and why was it modded Troll????).

Their initial attempt at ranking the choices didn't consider all the factors that go into the decision. Transitivity was never broken, just their model.

Re:Ranking choices consistently (1)

as.kdjrfh sxcjvs (2872465) | about 7 months ago | (#45967065)

Animals have to choose what to eat first, so a comparison operator is definitely applied to a collection of foods. The simple mathematical representation, which you are sticking to, is therefore the part we have to give up.

It's ineffective to abstract too early, and it's really ineffective to abstract into an inadequate framework.

Re:Ranking choices consistently (1)

Jane Q. Public (1010737) | about 7 months ago | (#45967413)

" think that they should not say that transitivity is broken but rather that the food attractiveness function can be changed by some events, thus reordering the elements in the set Foods."

But they didn't say that, because that would have been incorrect.

Indeed, transitivity does not always hold for inequalities, and this is a known mathematical fact. The article doesn't try to change that (as you suggest), but rather acknowledges that this phenomenon, in the context of preferences, can also be rational.

Make no mistake: many situations involving inequality do not display the property of transitivity. This is not a problem with the math, nor does it mean anything is "broken". There is nothing at all mathematically wrong with this. For years I have known of a game that is played by flipping a coin 3 times. You and someone else list your predictions of the result. Due to non-transivity of inequalities, no matter what combination you choose, I can choose one that has a better chance of occurring first. In other words, A > B > C > A (although there are actually 8 combinations, not just three).

Nothing is broken; the math is just fine.

Re:Ranking choices consistently (1)

CanHasDIY (1672858) | about 7 months ago | (#45965561)

"Think they do" != "do"

So, no, not 'the opposite,' but 'precisely what OP said.'

Re:Ranking choices consistently (1)

MightyYar (622222) | about 7 months ago | (#45966005)

I'm not sure what your point is. If you want absolute certainty, you probably aren't interested in science.

Re:Ranking choices consistently (1)

CanHasDIY (1672858) | about 7 months ago | (#45966089)

I'm not sure what your point is.

That researchers get shit wrong. A lot.

But they say, "well, we think it's this way," and a lot of people take it for gospel. That is, until some other group of researchers does another flawed experiment that produces another incorrect, different result. Rinse, repeat.

If you want absolute certainty, you probably aren't interested in science.

I'm less interested in absolute certainty, and more interested in having research done correctly, not biased or influenced by personal philosophy. Opinion has no place in the laboratory, unless we're experimenting on opinions.

Re:Ranking choices consistently (1)

MightyYar (622222) | about 7 months ago | (#45966391)

But they say, "well, we think it's this way," and a lot of people take it for gospel. That is, until some other group of researchers does another flawed experiment that produces another incorrect, different result. Rinse, repeat.

That's how we learn. Find the flaws in previous research and develop a new method without those flaws, fully understanding that you won't get it right either. The research is still useful, even if all it does is point out an area we don't fully understand.

Opinion has no place in the laboratory, unless we're experimenting on opinions.

OK, but I'm not sure why this paper is subject to that criticism.

Re:Ranking choices consistently (1)

CanHasDIY (1672858) | about 7 months ago | (#45966709)

Opinion has no place in the laboratory, unless we're experimenting on opinions.

OK, but I'm not sure why this paper is subject to that criticism.

All scientific papers should be subject to that criticism.

What can I say, I'm a born skeptic.

Re:Ranking choices consistently (1)

CanHasDIY (1672858) | about 7 months ago | (#45966147)

Relating to my previous response:

http://books.google.com/books/about/Bad_Science.html?id=znCisNI4c8MC [google.com]

Re:Ranking choices consistently (1)

MightyYar (622222) | about 7 months ago | (#45966435)

But this paper is in a respected, peer-reviewed journal. And it isn't being used to sell organic, cage-free, non-GMO pomegranates :)

Re:Ranking choices consistently (1)

CanHasDIY (1672858) | about 7 months ago | (#45966693)

But this paper is in a respected, peer-reviewed journal.

Article: Bogus science paper reveals peer review's flaws [www.cbc.ca]

And it isn't being used to sell organic, cage-free, non-GMO pomegranates :)

Maybe not, but I'd bet dollars to pesos that it is being used to sell the 'researchers' continued employment.

Re:Ranking choices consistently (1)

RazorSharp (1418697) | about 7 months ago | (#45966141)

I think you're both right, both saying the same thing, the OP just did so in a more cynical fashion. The important thing that the headline muddles is that there are no actual transitivity violations being observed, only seeming transitivity violations, so headline proposes something false ("why transivity [sic] violations can be rational').

Journalism wouldn't be interesting if the journalists understood the important minutiae of the scientific journals they refashion into pop articles.

Re:Ranking choices consistently (1)

MightyYar (622222) | about 7 months ago | (#45966329)

In defense of tomhath, the paper itself is a bit cavalier in its use of the word "transitivity"... it's not just TFA or the summary.

Re:Ranking choices consistently (2)

i kan reed (749298) | about 7 months ago | (#45965441)

And here we have someone whose biases are based entirely in the null hypothesis, using the null hypothesis to justify ignoring the conclusion. It's a good chance to see this behavior outside of its normal habitat of politics/religion.

Re:Ranking choices consistently (0)

Anonymous Coward | about 7 months ago | (#45965683)

the scientists didn't understand the criteria for ranking the choices

It's more complex than that. You make it sound like scientists were saying "hummingbirds are choosing foods by caloric intake", but in reality they're picking based on micro-nutrient content. But that's not quite the case. They've actually run the experiments where they independently present A+B, B+C, and A+C and see non-transitivity, and have presented A+B and A+B+C and see independence of irrelevant alternatives violations (e.g. picking A for A+B, but *B* for A+B+C). It shouldn't matter *what* criteria they're using for ranking - if they're doing a consistent job of ranking the choices, that shouldn't happen.

The issue lies in that phrase "ranking the choices". Both transitivity and independence of irrelevant alternatives make the implicit assumption that there's a single metric by which the choices can be ordered. That's not necessarily the case. Sometimes there a number of competing things which are important to consider, and there's no good single way to combine the various criteria into a single metric. Obviously you have to split that down and make a choice, but the way you do that doesn't necessarily equate to a weighted linear combination (or even a non-linear combination) of the various metrics. That doesn't mean, though, that the way of deciding between items with differing non-combinable sets of metrics is arbitrary or irrational - there's a logic to it, even if it isn't mathematically equivalent to reducing things to a single number.

This is relevant, by the way, to the comp sci jocks as well. There's various places in CS/IT where you have to do optimizations. The "conventional" optimization protocol mostly revolve around that same assumption - that there's a single number which you can use to label the fitness of the choices, and that metric consistently applies to all evaluations. Sometimes that assumption holds, but sometimes it doesn't. Sometimes the world is a little bit more messy than by-the-numbers geeks would like it to be. It's important to consider that sometimes it *isn't* that the system or people are behaving "irrationally", but that you may be over-simplifying things.

Re:Ranking choices consistently (1)

tomhath (637240) | about 7 months ago | (#45966445)

Sometimes there a number of competing things which are important to consider, and there's no good single way to combine the various criteria into a single metric.

Yes, but I still claim we're saying the same thing. Each action (hummingbird or whatever) is based on factors present at the time the decision was made. They had assumed they understood the relationship between choices A, B, and C, but it turns out there's more to it than they initially thought.

My cynicism is based on them bringing transitivity into the paper at all. It looks to me more like a linear programming problem rather than transitivity.

Transisviviisiity (1)

Anonymous Coward | about 7 months ago | (#45965223)

I'm sure the word "transitivity" feels rather violated by that ridiculously bad misspelling in the headline.

In other news: My security word is "fellatio." Just thought you'd all like to know.

First in with car analogy (0)

Anonymous Coward | about 7 months ago | (#45965225)

Car > Gas > Bike

Unless you have no Car, then Bike > Gas.

Really, the notion of interdependencies shouldn't cause a crisis in the laws of logic.

Re:First in with car analogy (1)

TangoMargarine (1617195) | about 7 months ago | (#45965391)

Two of those are forms of transport and one is a fuel. They're not directly comparable. One might argue that "Gas > Car" simply because gasoline has so many more uses. Cars...are only really good for one major use case. You could power stuff from their batteries, but that's really a functionality of the battery rather than the car.

Code monkey like tab AND mountain dew (1)

Z80xxc! (1111479) | about 7 months ago | (#45965229)

So basically, they discovered that humans aren't the only animals that enjoy variety in their diet?

Re:Code monkey like tab AND mountain dew (1)

CanHasDIY (1672858) | about 7 months ago | (#45965599)

So basically, they discovered that humans aren't the only animals that enjoy variety in their diet?

That, and/or they discovered that humans aren't the only ones who make decisions that seem unreasonable and arbitrary to a third party observer.

TL;DR version:

They discovered that humans are animals.

Re:Code monkey like tab AND mountain dew (1)

RazorSharp (1418697) | about 7 months ago | (#45966261)

That, and/or they discovered that humans aren't the only ones who make decisions that seem unreasonable and arbitrary to a third party observer.

Such as drinking crap like Tab or Mountain Dew. It may give you kidney stones, do a poor job of hydrating, lack vital nutrients, and only contain monomers which provide nothing more than short term energy, but it tastes sooo good.

Re:Code monkey like tab AND mountain dew (1)

CanHasDIY (1672858) | about 7 months ago | (#45966835)

Yesterday I tried to let my dog lick my cereal bowl; he sniffed it, turned away, and promptly began licking his backside.

I'm not really sure I want to know what makes a dog ass more appealing than a bowl of Kix...

Like playing lottery... (0)

Anonymous Coward | about 7 months ago | (#45965241)

This explains why so many people are playing powerball.

william poundstone gaming the vote (0)

Anonymous Coward | about 7 months ago | (#45965247)

I just read this book that covers voting theory and the spoiler effect and independent alternatives. For anyone who loves technical information delivered by a guy who makes it all sound human, William Poundstone is a must read author

http://www.nytimes.com/2008/03/20/books/20masl.html?_r=0

Finally some sense to being dumb (1)

cloud.pt (3412475) | about 7 months ago | (#45965265)

This will be the perfect excuse for every situation the human being can't explain his moral decisions, like why do we act stupid when in love, why do some people chose to go to war and why did they sack Conan from the Tonight Show.

Mood (1)

Russ1642 (1087959) | about 7 months ago | (#45965321)

There's just randomness in decision making sometimes. Get over it. Sometimes I just feel like stuffing my face with cheap pizza. Other times I prefer to skip dinner entirely.

Re:Mood (1)

RazorSharp (1418697) | about 7 months ago | (#45966351)

Maybe, although you're consciously unaware of it, your body craves the carbohydrates, proteins, and lipids that cheap pizza provides. And then other times, despite the fact that it's dinner time, you had a late lunch and you don't currently need any energy input, especially considering that you haven't used much energy sitting around browsing Slashdot.

There may be randomness in decision making sometimes, but basing a decision off of 'this is what I feel like' isn't random, you're just not making a conscious effort to employ logic (even though you probably do without realizing it).

Based on what? (3, Insightful)

gstoddart (321705) | about 7 months ago | (#45965323)

Organisms, including humans, are often assumed to be hard-wired by evolution to try to make optimal decisions, to the best of their knowledge.

What about humans have we seen to suggest humans are rational or are hard-wired make 'optimal' choices?

For biologists (or economists) to make this assumption has always struck me as terribly flawed, because in the real world, we see quite the opposite.

In the case of humans, cultural biases and any number of things skew our decision making to be less than perfect. And any theoretical model which assumes otherwise is pretty much the equivalent of assuming a perfectly spherical cow.

Re:Based on what? (0)

Anonymous Coward | about 7 months ago | (#45965663)

The important part here is " to the best of their knowledge"
Objectively it might not be the best choice, but from the viewpoint of the individual it is.

Re:Based on what? (0)

Anonymous Coward | about 7 months ago | (#45966467)

The important part here is " to the best of their knowledge"
Objectively it might not be the best choice, but from the viewpoint of the individual it is.

This is why psychologists are trying to develop a model for emotional intelligence, which often plays a bigger role in decision making than real intelligence. Consciously or not, we all make some decisions based on emotion and for some, it seems like most of them are made that way.

Re:Based on what? (1)

Oligonicella (659917) | about 7 months ago | (#45966575)

Bullshit. I know plenty of smokers who know it's bad for them. "To the best of their knowledge" only applies to humans and it fails.

Animals will also fall into habits that are not optimum, like getting drunk on overripe persimmons. The "knowledge" here is the survival of non-drunk members when the jaguar shows up.

The basic assumption is bogus.

Re:Based on what? (1)

umghhh (965931) | about 7 months ago | (#45965895)

TFA is badly written in this sense that so called irational is in fact not the way choices are made but our thinking about the choices themselves as it is apparently detached from the past and future. As in example they gave: if you usually have preference a b,c etc then in situation when different combinations are presented choices are still to be made consistently but apparent choices are not and the reason is not that the animal is less consistent but that the preference is not absolute but depends on the past so in fact you do not have only a,b,c but a occurring frequently of late and a occurring less frequently of late. So in reality you have 6 single options (in simple case) that can be mixed in different ways and decisions based on those.

Re:Based on what? (1)

Anonymous Coward | about 7 months ago | (#45965925)

There are basically two reasons for this.

One reason is that a rational actor is simple to model, as is the completely irrational actor. Altruistic is also fairly easy. Other models are tricky to define, let alone use.

The second reason is that the deviation from rationality may often be viewed as a stochastic variable with zero mean. Ignoring it affects individual cases, but not the overall conclusions.

But in this case, it seems that there are two ranking functions at play. There's the instant ranking: (if I now make a choice between A and B, it doesn't affect the future) and there's the forward-looking ranking (the ranking of choice A also includes the future impact). In general, those are not identical, and Rational Choice has no problem in dealing with that theoretical possibility.

Re:Based on what? (2)

hawkfish (8978) | about 7 months ago | (#45967003)

The second reason is that the deviation from rationality may often be viewed as a stochastic variable with zero mean. Ignoring it affects individual cases, but not the overall conclusions.

What is interesting about current research [nytimes.com] is that this assumption appears to not be true a lot of the time.

Re:Based on what? (1)

tlhIngan (30335) | about 7 months ago | (#45966479)

In the case of humans, cultural biases and any number of things skew our decision making to be less than perfect. And any theoretical model which assumes otherwise is pretty much the equivalent of assuming a perfectly spherical cow.

Hell, if you have two models of product, say, A and C, where A is better and more expensive than C, introducing a mid-range product B can skew sales towards A. I.e., if you have A and C, C sells more (generally because it's cheaper), but by having B, you can drive sales towards A. Even without having sold a single B. Or even an intention to sell B.

It's basic marketing and well-known for decades now. And you see it everywhere - from drink sizes, to menu choices, to your theatre (it skews sales towards the huge buckets of popcorn), and in product lines.

Just because (1)

MitchDev (2526834) | about 7 months ago | (#45965347)

A is better than B and B is better than C doesn't automatically mean A is better than C.

It would require more details and specifics.

When A and B are compared, the criteria that make A better than B doesn't necessarily make A better than C. The specifics and criteria used to judge/choose "better/preferred" need to be known as well.

Silly (and highly personal example):
A = Reese Peanut Butter Cups
B = M&Ms
C = Reese's Pieces

I like A more than B, and B more than C, but given the choice between A and C, I'd pick C.

Re:Just because (0)

Anonymous Coward | about 7 months ago | (#45965655)

The specifics and criteria used to judge/choose "better/preferred" need to be known as well

Those are described in the paper [royalsocie...ishing.org] (Possibly paywalled). They're talking about the optimal choice in terms of natural selection, and are assuming that the most energy per amount of time "handling" the food is best. They then throw in the possibility that some food options may only be transiently available.

If I've read it right they're saying that it's not always optimal to take the highest ranked food available at the time: if it takes you time to eat an item and other "better" items may appear and then disappear while you're doing that, it may be a better choice to ignore a "good-but-slow" item, spend less time eating a "lesser-but-faster" item and therefore make more decisions about what to eat per unit of time, giving you more opportunities to notice the best item suddenly appearing.

It's like only being able to take one plate off a sushi train at a time, and you can't take a new one until the last one is finished: you're hungry, so you have to take *something*, but it might be a better decision to take the crappy-but-fast items so that you're less likely to still be chewing if your favorite thing starts to roll past you, which is what would have happened if you'd taken the middle of the range but chewy clam sushi.

serious omissions in the reading (0)

nimbius (983462) | about 7 months ago | (#45965353)

Its important to reinforce the fact that violations in transivity, while rational, may never be appropriate under some circumstances.

in a TSA checkpoint. is your transivity under 3 ounces? did you remove your A and B before walking through C?
if transivity is for loading and unloading only. dont just put your blinkers on either or C will tow your A to B.
if you clicked through the EULA for windows 8 without reading, boy will you ever be sorry. You cant violate transivity or Internet explorer will responding. You could downgrade to B but A says you shouldnt otherwise you wont C your excel spreadsheets ever again..

News at 11 (1)

ledow (319597) | about 7 months ago | (#45965405)

Real life more complicated that contrived mathematical / logical model.

Re:News at 11 (1)

i kan reed (749298) | about 7 months ago | (#45965487)

More like "world defies 'common sense' solutions to problems", Which is amusing because you phrased it as one of those "common sense tells me this is obvious" type rejoinders.

Re:News at 11 (1)

TheCarp (96830) | about 7 months ago | (#45965593)

I just like pointing out that "Common Sense" is what tells you to put out a grease fire with water and steer your car out of a skid.

Re:News at 11 (1)

michael_cain (66650) | about 7 months ago | (#45966145)

Yep. Bad news for theoretical economics, which depends heavily on the assumption of transitivity or equivalent properties.

Girl analogy (0)

Anonymous Coward | about 7 months ago | (#45965527)

Super model > cheerleader > girl next door.
Given a chance to date A or C, choose C.

Maybe... (1)

XDirtypunkX (1290358) | about 7 months ago | (#45965693)

Without it, humans would have a heck of a time with rock, paper, scissors.

Totally flawed model (4, Insightful)

Kjella (173770) | about 7 months ago | (#45965749)

If you're trying to find a balanced diet using many ingredients and take one of those away, the rest of the diet might change totally. For example, let's assume the removed ingredient was a very good source of protein. Now you're scrambling to replace it with other protein sources, introducing foods you didn't need before. And now you're high on carbs, so your high-carb food goes out and is replaced by something else, so now you lack vitamin D so we add another new food and so on. It's a set ordering not a factor ordering because if you've eaten beef all week you'd rather eat pork, even if you prefer beef.

Re:Totally flawed model (1)

tomhath (637240) | about 7 months ago | (#45967275)

It seems like a resource optimization [wikipedia.org] problem, albeit a very difficult one to model.

some animals (1)

Megane (129182) | about 7 months ago | (#45965931)

But sometimes animals do not display such logic.

Such as pokemon, who have non-transitive strengths and weaknesses like in the game Rock Paper Scissors. [wikipedia.org]

Wait so... (1)

Jizzbug (101250) | about 7 months ago | (#45966217)

It was irrational to think this behavior was irrational?

If you think you've found a conflict... (0)

Anonymous Coward | about 7 months ago | (#45966229)

Researchers discover their premises are too simplistic to model the real world. Whenever you think that you are facing a contradiction, check your premises.

Barely linked to evolution at all (1)

badasawsomeness (3025411) | about 7 months ago | (#45966323)

Evolution does not dictate that an animal will always instinctively do what will extend its life. There are numerous examples of simple traps humans set where the animal could easily escape if it would give up the bait but they deliberately stay tapped. Animals introduced to new environments have been seen ingesting toxic plants. People obviously do many things that are harmful to their health.

Evolution says that nature will breed out traits that did not extend an animals life. Giving a dumbed down example, say a person was allergic to smoking, ad say this was passed down to his children. By not smoking him and his children would live longer lives thus giving them more opportunities to breed, and over thousands of years you might see an increase in people allergic to smoking because it naturally allowed people to live longer, it became an evolved trait.

Evolution does not work on this micro scale of every day decisions an animal decides to make. Animals to do have some psychic knowledge to be introduced to two new food and instantly know which has the optimal nutrition.

Speling much? (0)

Anonymous Coward | about 7 months ago | (#45966475)

Do you guys even look at your posts before you commit them? Sheesh.

It's always rational (1)

xyourfacekillerx (939258) | about 7 months ago | (#45966509)

I don't know if this is a good application of the word "rationality".

"My logic was not in error... but I was." (1)

tersegon (3384503) | about 7 months ago | (#45966559)

One of the counterexamples given here, in which the organism anticipates a future shortage, is not a situation in which transitivity is violated. In this case the organism is acting on a lack of knowledge of the future and playing it safe. This is not a failure of the logic of transitivity, but a great accomplishment of life: the ability to accept that one doesn't have all of the information and to manage regardless. The authors are essentially doing the same thing by suggesting that our preconceptions of logical behavior don't cover all situations!

The gist of what's going on (0)

Anonymous Coward | about 7 months ago | (#45966601)

The comments on this story indicate that nobody has read the article or its citations, so here's a better summary for those of us who don't want to read the article.

First, the experimental evidence: While the paper linked to in the summary is in fact a math paper (and thus has no new experimental resutls), it does cite a few science papers, of which the best [springer.com] describes a real experimental setup:

Gray jays (Perisoreus canadensis) collecting food for storage violated this principle, and failed to support even weaker forms of transitivity. All subjects preferred option a (one raisin, 28 cm into a tube) over b (two raisins, 42 cm), and b over c (three raisins, 56 cm), but none of the subjects preferred a over c.

So we do have something concrete. Some birds are put in front of some tubes that have raisins in them. Some tubes have a few raisins near the front of the tube (easy to reach) and others have a larger number of raisins that are towards the back of the tube (difficult to reach). The birds must then evaluate the distance-versus-quantity tradeoff: is it worth crawling a little deeper into the tube to get more raisins? Birds were given three tubes to choose from and, like the article summary says, they thought tube A was better than tube B and that B was better than C, but they thought C was better than A.

What kept the birds from entering both tubes? Unfortunately, I don't know, but if someone will send me $40 I'll buy the Springer article and find out.

There was another experiment done on hummingbirds [sciencedirect.com] that did what the authors call a "binary/trinary" procedure: Three different types of fake flowers were created. All flowers were given sucrose in water, but the concentration of sugar and the total amount of available liquid varied between flowers. In A-type flowers, there was a small amount of high-concentration sugar water. In B-type flowers, there was a large amount of low-concentration sugar water. Then there were C-type flowers, which were strictly inferior to A-type flowers (less water and a lower concentration of sugar!) but only partially worse than B-type flowers (less water, but a higher sugar concentration). Then four experiments were run: Three binary experiments (where birds choose between A and B, between B and C, and between C and A), and one "trinary" experiment (where birds were given all three flowers at the same time). The binary experiments showed that birds consistently picked A over B, B over C, and A over C. That's perfectly consistent. But in the ternary experiment, six of sixteen birds decided that B was the best of the three. That's a violation of regularity because if A-type flowers are better than B-type flowers, then it shouldn't matter whether or not C-type flowers exist.

So... We have some experiments suggesting that birds don't rate their food sources consistently---what they pick depends on the context. There are a couple of ways to deal with this. One is to insist that an experiment on sixteen birds is too small to conclude anything (which is true) and therefore is too small to suggest that something is worth further investigation (which is silly). Another is to agree that the experiment shows that there's something complex about the way that birds rank their food sources, but to insist that it's non-news because "everybody knows the world is complex and that cows aren't spherical." That's a fascinating viewpoint---you could use it to trivialize all of science. Still another response is to make a post on Slashdot about how your options vary based on what's available because you need balanced nutition---at least you're thinking, but all of the experiments are careful to balance a single food type (e.g. raisins, sucrose) against a non-nutritional parameter (e.g. distance, concentration).

The authors of the present paper decided to present one mathematical model that covers both types of experiments, and also addresses the fact that birds don't have to choose between A and B; they could easily take both, and they really need only choose which one to take first. That's the point of the paper. If you put a bird in front of a bunch of food sources, the bird has to decide on the sequence in which it eats. In a simple world, the bird could estimate the cost-to-benefit ratio of each tube individually, then start with the best tube and work down the list. But that isn't optimal in nature because while you're eating the most efficient food source, something bad might happen to your second choice on the list. (Maybe it will be eaten by another bird.) So you need a new strategy.

Tables 1 and 2 in the cited paper explain how their model works. There are three food sources: A, C, and B. (Sorry for the weird order; I want to match the paper.) Source A is like twenty raisins in the back of the tube: It gives you the most nutrition but it takes a very long time to get to it. Source C is like eighteen raisins only halfway down the tube. For about half the effort, you get 90% of the nutrition. Source B is just eight raisins about 25% of the way down the tube--for a quarter of the effort, you can get 40% of the nutrition. (Remember: These are three different tubes!) But there's an extra consideration in this model: The food sources appear and disappear while you're crawling back out of the tube. So if you pick food source A, you're guaranteed to get it, but there's a chance that tubes B and C will disappear when you're crawling back out. Once you're out of the tube, you pick your second food source from whatever options are still available. To make things interesting: Food sources A and C have a high probability of disappearance; source B has a very low one.

Applying this to the gray jays, we get a situation where the raisins in the front are better than the raisins in the middle, and the raisins in the middle are better than the raisins in the back. So far, so good. But what if you have to choose between the raisins in the front and the raisins in the back? There's a good chance that after eating the front raisins, the back raisins will disappear, and the front raisins aren't enough to survive, so you take the back raisins. If all three tubes are available, it's safer to pick the front raisins because the middle raisins are likely to still be there when you're done.

I have to get back to work so I can't write a smooth-sounding conclusion paragraph. Sorry!

Transitivity in action (0)

Anonymous Coward | about 7 months ago | (#45966677)

Nothing is better than anything.
A ham sandwich is better than nothing.
Therefore, a ham sandwich is better than anything.

Hierarchy? (0)

Anonymous Coward | about 7 months ago | (#45966761)

yeh .. but reality isn't hierarchical. Hierarchy is a sometimes convenient projection. And othertimes a misleading projection.

Eg. quite often: A is preferred over B; B over C; and C over A.

Where is your Transivity, now?

Monty Hall (0)

Anonymous Coward | about 7 months ago | (#45966781)

Not totally unprecedented. The Monty Hall problem (http://en.wikipedia.org/wiki/Monty_Hall_problem) shows is that removing something changes the nature of the problem. It is essentially gives us extra information.

Spherical chickens in a vacuum (0)

Anonymous Coward | about 7 months ago | (#45966837)

Academic ideas based on simple assumptions fail to model the real world accurately. Film at 11.

Nice to know the economics department isn't the only one with this problem.

This explains why people order a McRib ;^p (1)

slew (2918) | about 7 months ago | (#45967307)

I always wondered why people ordered McRibs.

It certainly can't be consistently ranked better than anything else on McD's normal menu, yet people seem to irrationally still buy them.

Maybe this explains it... Nah... ;^P

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