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Why Transitivity Violations Can Be Rational
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."
... any given food source.
In other words, the scientists didn't understand the criteria for ranking the choices. Nothing to see here...
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.
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.
So basically, they discovered that humans aren't the only animals that enjoy variety in their diet?
This explains why so many people are playing powerball.
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
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.
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.
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.
Lost at C:>. Found at C.
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.
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..
Good people go to bed earlier.
Real life more complicated that contrived mathematical / logical model.
Super model > cheerleader > girl next door.
Given a chance to date A or C, choose C.
Without it, humans would have a heck of a time with rock, paper, scissors.
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.
Live today, because you never know what tomorrow brings
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.
#naabhaprzrag, #sverubfr-000, #agi-fcbafberq, negvpyr[pynff*=' negvpyr-ary-'] { qvfcynl: abar !vzcbegnag; }
Researchers discover their premises are too simplistic to model the real world. Whenever you think that you are facing a contradiction, check your premises.
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.
Some drink at the fountain of knowledge. Others just gargle.
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.
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.
Some drink at the fountain of knowledge. Others just gargle.
Do you guys even look at your posts before you commit them? Sheesh.
I don't know if this is a good application of the word "rationality".
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 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 describes a real experimental setup:
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 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 mathematica
Nothing is better than anything.
A ham sandwich is better than nothing.
Therefore, a ham sandwich is better than anything.
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?
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.
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.
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
Hasn't the author ever played Rock, Scissors, Paper? (or, for that matter, Rock, Scissors, Paper, Lizard, Spock).
Unpredictability is a necessary trait when evading predators, so an organism that always chose C when C > B and B > A would be more predictable and easier for an intelligent predator to catch. This tendency not to would need to be deeply hardwired into the nature of the organism, since otherwise it would rarely kick in and, again, the organism would be easy prey. Optimising a small subset of a problem (and the whole problem is survival and procreation) often leads to locally optimal yet seriously globally subobtimal solutions. The greedy algorithm works on only a few cases (sometimes called monoids if I remember my combinatorial optimisation text, though that was over a decade ago); and with only slightly more complex problems it is often easy to construct pathological cases where the greedy algorithm gets it wrong. I see this result about organisms as another example of the principle that straightforward rational solutions are only the best when the problem is straightforward and simple.
John_Chalisque
the birds and the bees...
In other news, there is more than one dimension!
-I like my women like I like my tea: green-
Hammer is better than a screw driver at pounding in a nail. Screw driver is better than a pillow, so logic would say hammer is better than pillow.
So is the hammer *always* better than the screw driver or nail? No.. what if it's a screw you're using? Yes, you COULD pound it in with a hammer but that's going to suck and ruin the holding power.
It should be common sense A > B > C but sometimes B > A in other circumstances.
Must humans are most definitely not hard-wired by evolution to try to make optimal decisions. Most humans are very bad at making optimal decisions, most decision we make are the opposite I'd say.
I use the same logic when your wife is available along with a selection of other ho's.
Your wife will keep until last as she is unlikely to be selected while there is another choice.
Or is it your wife who applies this logic to you?
Karma is a scorned bitch.
Further, transitivity assumes there is no hysterisis. Every decision is made in vacuum or from a pristine starting state. That is definitely not the case of organisms. Especially recent memory being more dominant than distant memory. So when the relative advantage of A over B, B over C, A over C etc are not significant, the organism would choose based on recent experience.
sed -e 's/Chuck Norris/Rajnikant/g' joke > fact
Scientist always thought that choices made by animals could be modeled using simple algorithms such as if A is preferred over B and B is preferred over C, then if A and C is offered the animal would choose A. When the animal being observed didn't choose A they declared a transitivity violation. What they have discovered is that there model was flawed and what goes into making one choice better than another is more involved than first thought. As such, there is not transitivity violation and the animals still always make the best choice for the given circumstance.
This is what I come to Slashdot in hopes of reading.
Everything, from from purely natural processes such as water flowing down hill to very complex behaviors like walking or food choices follows the same rule:
Minimum Energy.
With A > B > C, there is an ordering along a single dimension. Reality has many more orderable dimensions, which allows for optimal "non-transitive" solutions. Along one criteria, A>B>C, whereas along a different criteria C>B>A.
Take Olympic atheletes as an example. Let S be a 100 m sprinter, let P be a shot-putter, and let D be a decathlete. In speed, S>D>P. In throwing distance P>D>S. In long-jump D>S>P, and so on.
If I had to pick a group of athletes to complete a task, my choice changes depending on the task.
Quoting George Santayana, "Those who do not know history are condemned to repeat it." It has been known since the late 18th century that transitivity is not rational, however much economists and others would like to think otherwise. See Condorcet's paradox for details.
I had a prof who would take a vote on which day we would have our test. Once he gave us the choice of next week monday or friday. The vote was overwhelmingly monday (I can't remember but something like 2/3). Immediately after he realized that wednesday was also an option, so we had a re-vote. Friday won out with a majority (not plurality) vote.
So, no, I don't think that guans are wired for logical decision making. Animals, I still hold out hope for.
Take a simple game of dice. Each person roles one dice and the bigger number wins. You can make 3 dice (A, B, C) so that A wins against B, B against C and C against A more often than not.
Note: You don't cheat on the dice, they are perfectly balanced. The trick is what numbers you put on the sides.
Who exactly assumes this. If you think this is how evolution works, you don't understand evolution. If you think this is how the human brain evolved to function, you don't understand evolution or what is known about neurobiology.