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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."
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.
So basically, they discovered that humans aren't the only animals that enjoy variety in their diet?
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.
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.
http://www.beanleafpress.com
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.
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.
W..w..W - Willy Waterloo washes Warren Wiggins who is washing Waldo Woo.
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.
Unity? Screw that: XFCE. Slashdot Beta? Screw that: SoylentNews. Australis? Screw that: Pale Moon. UX developers DIAF
Real life more complicated that contrived mathematical / logical model.
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.
If your wife reads Slashdot this little game could end quite badly... never get between a woman and her chocolate!
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.
"I opened my eyes, and everything went dark again"
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.
Might as well face it I'm addicted to data.
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...
An enigma, wrapped in a riddle, shrouded in bacon and cheese
"Think they do" != "do"
So, no, not 'the opposite,' but 'precisely what OP said.'
An enigma, wrapped in a riddle, shrouded in bacon and cheese
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.
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.
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
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.
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).
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; }
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.
I'm not sure what your point is. If you want absolute certainty, you probably aren't interested in science.
W..w..W - Willy Waterloo washes Warren Wiggins who is washing Waldo Woo.
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.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
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.
"From the depths of my skeptical and rationalist soul, I ask the Lord to protect me from California touchie-feeliedom."
Relating to my previous response:
http://books.google.com/books/about/Bad_Science.html?id=znCisNI4c8MC
An enigma, wrapped in a riddle, shrouded in bacon and cheese
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.
Violence is like duct tape. If it doesn't solve the problem, you didn't use enough.
C'mon that was obviously a joke... How cranky can one be?
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.
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.
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.
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.
W..w..W - Willy Waterloo washes Warren Wiggins who is washing Waldo Woo.
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.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
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."
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.
W..w..W - Willy Waterloo washes Warren Wiggins who is washing Waldo Woo.
You are the most knee-jerk racist hiding in a "liberal" sheep's coat that I've ever read comment here.
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.
But this paper is in a respected, peer-reviewed journal. And it isn't being used to sell organic, cage-free, non-GMO pomegranates :)
W..w..W - Willy Waterloo washes Warren Wiggins who is washing Waldo Woo.
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.
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.
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!
What a jerk!
But this paper is in a respected, peer-reviewed journal.
Article: Bogus science paper reveals peer review's flaws
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.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
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.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
Do you not realize that in saying things like "femi-nazi," you are one of the cranks you deride?
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...
You will not drink with us, but you would taste our steel? - Walter Matthau, The Pirates
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.
Do you not realize that "opinion != fact?"
Besides, I never disqualified any 'Murican from being a crank, present company included.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
purposefully
Purposely. Purposefully means something else.
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
" 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.
Maybe you need to refresh the definition of a comparison operator : Partially Ordered set. In short : you can not have an ordering comparison relation and not having transitivity for it. Period. So either it is an ordered set (like \mathbb{R}) and you can use a comparison operator or it is not (like \mathbb{C}) and you cannot use any ordering relation.
hum, my bad : the following link is missing : http://en.wikipedia.org/wiki/Order_theory#Partially_ordered_sets
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
There is great value in looking at behavior that appears to be irrational and trying to figure out what unconsidered factor makes it rational after all.
For example, the pandas. It may be that their dietary choice is a problem for them now, but prior to the dominance of another species that can and will slash and burn a whole forest, if you're going to depend on a single food, one that grows so fast you can sometimes actually see it growing isn't a bad choice.
Similarly, the potato monoculture decision in Ireland wasn't irrational, it was just made before some very important factors were known.
Maybe you need to refresh the definition of a comparison operator : Partially Ordered set. In short : you can not have an ordering comparison relation and not having transitivity for it.
Maybe you need to brush up on your inequalities. I assure you that in the real world some inequalities (such as preferences) are not transitive. I have already explained one situation in which that is true, and you can prove it for yourself.
Flip a coin 3 times. Write down the result: HHH, THT, etc. There are 8 combinations. The game is played this way: you write down your prediction. I write down mine. NO MATTER WHICH prediction you make (if of course you make it first), I can choose another combination that has at least a 2/3 probability of occurring before yours. This is non-transitive, because (if you label the combinations with letters), it means A > B > C > D > E > F > G > H > A.
In fact, here is a chart of the probabilities of one combination coming up before another.
You need not believe me; you can flip a coin a few thousand times and prove it for yourself.
Then, if you still don't believe... I have a game I'd like to play with you. $5 a round.
The upshot is this: no matter what set theory may be telling you, non-transitivity of inequalities DOES occur in real world situations, and if you refuse to believe that, you'd better not be a gambler.
The two things that he was referring to were "eating chocolate" and "being skinny". Which, pretty much are mutually exclusive to men and women alike....
"I do not agree with what you say, but I will defend to the death your right to say it"
the birds and the bees...
They are using the word "rational" to describe a specific, common-sense-to-humans, transitive property of preferences. That is all. You are reading way to much into their choice of words. The whole point of evolution by natural selection is that certain traits emerge because they are adaptive. What this paper sets out to show is that the behavior we see is not "rational" in the common sense, but it is still adaptive. It did not evolve "due to an absurd amount of chaos." They're basically arguing that long-term adaptivity trumps short-term logic.
Really there's a pretty good allegory to human behavior here. People frequently prefer to do things that are not in their long-term best interest, because they only think about their short-term best interest. Eating your second-favorite chocolate first could lead to your wife only buying milk chocolate, since you obviously like it better. Shooting the guy in the row in front of you might seem like a good way to get him to stop texting, but it's a terrible way to enjoy the rest of your movie. Faking being in the CIA might sound like a great way to get a nice paid vacation, but you will eventually get busted. Groups of people (think governments) are particularly bad at this, too. If I list any examples, I'll get modded as flamebait, but I'm sure you can think of several.
You know, I never liked the fried chicken or watermelon stereotypes. Who the hell doesn't like fried chicken or watermelon?
Anyway, stereotypes exist because someone observed that, on average, foo is true of a significant portion of demographic bar. They simplify decision making at the expense of some accuracy.
Like many things, there are times when stereotypes are useful and times when using them is a dick move. Recognizing that a fair majority of women like flowers and chocolate is generally fine to both use and say. Recognizing that a good percentage of pregnant women are often freaking insane is impolite to say but you'd damned well better be prepared to deal with it if you're married to one.
Recognizing that most anyone replying like you did is a self-hating lib who cares about feelings more than truth and logic, that one's just too easy.
Violence is like duct tape. If it doesn't solve the problem, you didn't use enough.
Rock smashes Scissors.
planet texture maps and more
Clarification: you are supposed to write down your predictions first, of course. That's why they're called "predictions". THEN you flip the coin 3 times.
In other news, there is more than one dimension!
-I like my women like I like my tea: green-
I thought you were trying to say that such non-transitivities are a fiction.
But instead (I think) you are saying that a new notation should be found for them?
I would argue that the problem isn't with transitivity, but with assuming that value is fixed around objects. In reality, value fluctuates according to circumstances.
I might give you $100 for your bar of dark chocolate because I love it that much and I don't have any. But if I have 5 tons of delicious dark chocolate in my basement, I'm not going to give you even $1 for your bar.
In programming parlance, it's the difference between
int value = darkChoc.Deliciousness();
and
int value() { return darkChoc.Deliciousness(); }
All my liberal friends think I'm a conservative, all my conservative friends think I'm a liberal.
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.
Some people just don't know tongue-in-cheek humor when they see it.
But the TSA is a Travesty, not a "transivity"....
And I'm just supposed to take your word on that?
OK, let's see : I am not familiar with this game and I don't know if you your selection and random event are ordered (not in the sense of the discussion on the sets we have but on the order of the events to appear : if I say, for example, 'HTH' does the sequence of random events must exactly match 'HTH' or 'HHT' and 'THH' are also considered a match)?
For the following few lines I will consider that this is true (while I think that it is false from the table you gave, but I don't think that it is changing anything on the model of the game we are debating on, correct me if I am wrong) :
Lets try to re-write in terms of clean Mathematics (boring but needed) : let P the set of possible events, P = {HHH, HHT, ..., TTT}. The first player 'A' take an element called C_A form this set and, then, the second player chooses a element C_B from the set P\C_A (P set from which we remove C_A). Simple statistics (for balanced coins) give us that the probability of player A to win the game is 1/card(P) = 1/8, while the player 'B' has 1/card(P\C_A) = 1/7. We have then Pr('A wins on choice of C_A \in P') if(C_A==C_B) then return 1/card(P) otherwise return 1/(card(P)-1). This does not order the set as all weight are equals but not all the elements are equal (thus the set is not ordered by this relation). For example, we have f_HHH(HHT)=f_HHH(HTT) but not HHT==HTT.
Now I will try to conclude on the approach of the Food model (and the set named Foods) : the fitness function f_Contex(food) carries a Context variable that changes the score of each food. The Context can be adapted to the Nature and changes the favor the animals give to some source so if f_Context1(food_A) > f_Context1(food_B) > f_Context2(food_C) then it is more likely that for a large number of animal, they will choose food_A (mean). but this can change upon context change and have a reordering to f_Context2(food_B) > f_Context2(food_C) > f_Context2(food_A) without breaking transitivity in real world. It is just about finding a general enough model for the fitness/cost function (which is, I agree, very complex and probably impossible to reach). Then you have to rely upon some sort of piece-wise fitness functions, or I should say context-wise fitness function.
Normally I'd agree, but considering the context here, I think it works either way.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
The two things that he was referring to were "eating chocolate" and "being skinny". Which, pretty much are mutually exclusive to men and women alike....
You're cherry picking. Fact is, OP made a broad generalization about women, and I called them on it. If you're getting anything else out of my comment then it's something you've come up with on your own.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
No, you're the one saying that stereotypes can never be accurate. They often can be- especially when they're of the form: __ likes $DeliciousThing.
You know, I never liked the fried chicken or watermelon stereotypes. Who the hell doesn't like fried chicken or watermelon?
I'm with you on the fried chicken part, but personally I've never been a big fan of watermelon.
FTR, the black people/watermelon stereotype is less about liking the fruit, and more about stealing them. Not sure where it originated, but I have seen a gum adverts from the early 20th century that depicts a black-faced child sneaking under a fence to snatch a melon or two. Can't seem to find it on Google, though...
Anyway, stereotypes exist because someone observed that, on average, foo is true of a significant portion of demographic bar. They simplify decision making at the expense of some accuracy.
Some stereotypes exist because of observed behavior. Some exist because of preconceived notions based on no observation whatsoever, but rather bigotry.
I hate generalizations, because they're always wrong.
Like many things, there are times when stereotypes are useful and times when using them is a dick move. Recognizing that a fair majority of women like flowers and chocolate is generally fine to both use and say.
"Recognizing a fair majority," sure. But that's not what OP did when he said "ask any woman..." He generalized, in a way that I know to be untrue, and so I called him on it.
And then, somehow, got into a semantics argument with, like, 10 other people. Only on Slashdot.
Recognizing that a good percentage of pregnant women are often freaking insane is impolite to say but you'd damned well better be prepared to deal with it if you're married to one.
OK, disregarding stereotypes, generalizations, and all that for a moment - never, ever put the words "insane" and "pregnant woman" together when you're within arms reach of one. Unless you're a masochist, in which case, have fun!
Recognizing that most anyone replying like you did is a self-hating lib who cares about feelings more than truth and logic, that one's just too easy.
But see, there's the fallacy - you say that my response is stereotypical of a 'self-hating lib,' but as I am decidedly not one of those people, the stereotype is demonstrably proven false.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
Judging by the rhetoric, that seems to be precluded. There was a clear implication that the wife somehow has claimed all dark chocolate in the relationship, as gynocentrically chauvinistic as that is. Speaking of realistic stereotypes that'll set off the feminazis...
"A soft answer turneth away wrath. Once wrath is looking the other way, shoot it in the head."
No, you're the one saying that stereotypes can never be accurate.
Did I say that? I was pretty sure my exact words were
Stereotypes generally exist because...
Which, through the use of the modifier "generally," would imply that I feel most stereotypes are inaccurately based on bigotry, but not necessarily all.
Although, if I did make such a generalization, I hereby retract is, since all generalizations are inherently false.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
"For the following few lines I will consider that this is true (while I think that it is false from the table you gave, but I don't think that it is changing anything on the model of the game we are debating on, correct me if I am wrong) :"
Pardon me. You are correct: I did not describe the game properly. Let me start from the beginning.
We agree that there are 8 possible combinations that can occur in 3 coin flips: HHH, HHT, etc.
The way the game is played is that player A chooses one of those combinations, and player B chooses one of those combinations (presumably a different one; there would be no point in choosing the same one). Then a coin is flipped until one of those combinations appears. The winner is the person whose chosen combination appears first (at which point the game stops).
It is easy to show that as long as B chooses after A, the probabilities are non-transitive. I.e., no matter which combination is chosen by A, player B can always choose a combination that has a higher probability of appearing first. Therefore you have a truly non-transitive situation. There is no single choice A can make that does not allow B to choose another with a higher probability.
Again, since if B is knowledgeable and chooses in order to maximize his probability of winning, the minimum probability that he will win is 2/3, so it is not at all difficult to demonstrate this non-transitivity in the real world. For example, it is easy to show that in any sequence of coin flips, there is a probability of 7/8 that THH will appear before HHH. But if player A chose THH, it is again easy to show that player B has a 2/3 probability of winning by choosing TTH. And round it goes.
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.
This didn't make any sense until i looked it up and saw that you're predicting a subsequence of continuous throws. Just thought I'd point that out in case anyone else was confused.
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.
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?
The logical fallacy I'm worried about is expecting an experiment to display only a bias for "efficient food gathering". It could be that the extra energy spent in wandering farther for food may be worth it in a natural setting to avoid predators, or avoid stale food, or the exercise may aid in digestion. Maybe the birds liked to hide in the tube, maybe some thought they'd feel trapped. Other people have made plenty of other observations on this post with alternate theories, but there are many many possibilities not related to the one variable the authors controlled for. It may even be due to nothing at all... just a ghost in the machine so to speak that wasn't weeded out via evolution because the birds were efficient enough to survive, eat, and spend lots of energy on other goals.
Expecting Occam's Razor to apply to complex systems in the most trivial ways is part of the mistake. I'm glad the research is done, it IS interesting and I generally approve of expanding knowledge. My complaint is that the author seems so surprised, and that I frequently see this sort of surprise and reasoning lead to or come from an anthropomorphism of evolution (i.e. assigning "intent") where I just don't think it applies. We behave as if evolution selected for specific traits (like those Big Three) because we witness the system in reverse, but if we had evolved into immortal asexual resource-unconstrained, we may see it differently. The underlying mechanisms would have been the same, though -- evolution need not have intent, goals, or this sort of anthropic rationality driving it to be effective and fascinating, and worth studying.
Uhh... including that one?
Requiem for the American Dream
Yep, cognitively we make general rules then hang a few exceptions on the rule then when the number of exceptions gets too large, we modify the rule.
Requiem for the American Dream
My wife has also said the exact same thing.
Sometimes it's good to know when to quit. Just saying :D
Requiem for the American Dream
Uhh... including that one?
That's a statement of fact. Good catch nonetheless.
The quote, BTW, is "Most generalizations are false, including this one." I'm guessing Mr. Clemens may have come up with that after having a similar conversation to the one we're having now.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
Of course, it's ironic, isn't it?
Something which seems to have been ignored for most of this thread.
Requiem for the American Dream
You know what my wife says?
"If you treated me like that, you wouldn't be married."
Sometimes it's important to remember that the plural of anecdote is not evidence.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
Of course, it's ironic, isn't it?
No; it's coincidental.
Irony, for the record is "the expression of one's meaning by using language that normally signifies the opposite, typically for humorous or emphatic effect."
Example: "Dude, I am soooo enjoying this root canal."
Something which seems to have been ignored for most of this thread.
OK, yea, that one I've got to give to ya.
An enigma, wrapped in a riddle, shrouded in bacon and cheese
I know this is a joke, but I suspect you're an ass regardless. I mean, he's the one who eats more chocolate, because he actively consumes her share in order to enlarge his overall supply, and she's the fat one?