Can irrationality be the rational choice?

Great Debates
1

I just read Priceless by William Poundstone. It’s about psychology and economics. A good book worth reading.

In this book, Poundstone makes several references to the ultimatum game, which is a common “game” used to study economics. The thing is, by economic theory, people don’t play the game correctly.

The rules of the ultimatum game are simple. You have two people and a sum of money (usually ten dollars). The first person divides up the money into two shares; one for himself and one for the second person, with whatever amount he wants in each pile - he can even put all the money into his own pile if he wishs.

The second player is then told how much money there is in the two piles. (The two players do not communicate and usually do not even meet each other.) The second player can accept of decline. If he accepts, both players get the money in their pile. If he declines, neither player gets the money in their pile. (And it’s a one-time game. You don’t get further chances to play.)

Now according to most economic theories, the rational thing for the second player to do is to accept whatever he’s offered. He invested nothing in and both options take the same amount of effort, so anything he receives is a clear gain. Even if he’s told that his pile contains one cent and the first guy’s pile contains $9.99, he’s still better off taking the penny than refusing it.

And, rationally, if the second guy will accept any offer, regardless of how small his share is, then the first player should maximize his reward as much as possible, He should only offer the second player one penny in order to keep the rest. It’s not like either player has a better moral claim to the money. The first player’s just in lucky position to get a larger windfall than the second player is.

But, as many of you are probably thinking, the game usually doesn’t work out this way in actual practice. It’s very rare for the first player to offer the maximum/minimum split. And in cases where it is offered (or where the offer is judged to be too close to the maximum/minimum split) the second player will usually decline the offer even though he loses whatever amount he would have received. So both players appear to be playing the game irrationally. And economists and psychologists put a lot of effort into explaining why.

But my question is whether there actually is a problem here that needs explaining.

Suppose you’re a human ambassador to outer space and you’re involved in some diplomatic negotiations that are analogous to the ultimatum game.

You might be negotiating with the Vulcans. They’re known for being completely rational, logical, and emotionless. They don’t do favors and they don’t hold grudges. They’ll take whatever they can and give up whatever they have do.

Or you might be negotiating with the Romulans. They’re known for their sense of honor. They will take offense to anything they perceive as an insult and are willing to defy any odds against them rather than ignore a slight.

So if you’re in the first position with the Vulcans, you’re going to offer them the bare minimum. You know they’ll do the rational thing and accept this minimal offer. But if you’re in the first position with the Romulans, you’re going to offer them a 50/50 split. Anything less and you know they’ll do the irrational thing and refuse the offer even though it’ll hust them as well.

Look at what happens. The group that does the rational thing to maximize its rewards ends up with minimal rewards. The group that is willing to not do the rational thing to maximize its rewards, actually ends up with much greater rewards.

But, and here’s the kicker, doesn’t this mean that not doing the rational thing is in fact the rational thing to do? The irrational people got more than the rational people. So wouldn’t the rational people see this and rationally decide that they should act irrational in order to increase their rewards?

And, as I said, these same results apply in real life in ultimatum games played by real people. So the economists who are trying to explain why people aren’t playing rationally are missing the fact that they are playing rationally.

2

Sure. I’ve heard it called being “rationally irrational”; being irrational in the right way at the right time. Part of it is a matter of thinking outside the system; if the rules of the game mean that rational people will do worse, then the rational thing on a meta level is to be irrational within the rules of the game; such as a bunch of prisoners in a “Prisoner’s Dilemma” situation all keeping to an oath of silence regardless of any promises or threats from their captors. And part of it is the related problem that other people are quite capable of “gaming the system” and setting up situations where the “rational” choice is to do what they want.

3

In the money game, the two sides know only the amount divided up, they nothing about each other. They will not even meet. Walking away from a penny is no big deal. Maximizing a reward? A negligible reward is no reward in the minds of most people, especially when they know it is negligible because of another person’s greed or stupidity.

The situations with the Vulcans and Romulans contain extra variables, so they are not equivalent to the money game.

You are stuck on rationality being something it is not. In certain situations doing what appears at first to be irrational is the rational thing to do. The irrationality is not really irrational.

4

Heh. Reminds me of the example our professor stymied us with: imagine you’re playing chicken; first driver to swerve away loses, and if neither swerves you’ll both crash into each other. And right as your cars start heading for each other, the other guy – throws his steering wheel out the window.

5

No. The Romulans’ improved outcome is due to a reputation for irrationality. There’s nothing irrational about deliberately fostering such a reputation if it will provide an advantage. In fact, having a reputation for being irrational because you’re irrational will produce worse results than having a reputation for being irrational because you’re rational.

6

Reality, unlike most bits of game theory, is almost always iterative. If you iterate the Ultimatium game, you quickly determine that the optimal solution is one in which the other guy can’t parlay his greater winnings into leverage over you; it’s in your long-term best interests to keep things as equitable as possible. So, it’s rational, in the real world, to divvy things up fairly.

7

cool!
:smiley:

8

I don’t see anything irrational in the ultimatum game, when the player B declines the one cent pot.

He is faced with a choice between (a) having the satisfaction of acquiring one cent, and (b) having the satisfaction of not co-operating in what he sees as a unfair abuse of arbitrary power by player A. It is rational for him to choose whichever of these two gives him the most satisfaction.

When we describe choice (a) as the rational choice, we are making an implicit assumption that the material satisfaction of having one cent always outweighs the intangible satisfaction of asserting a moral viewpoint. There is no basis for this assumption and, in fact, it is easily shown to be false. If it were true, nobody would ever donate one cent a charity for the benefit of people they did not know.

9

Three things.

  1. You yourself showed why it doesn’t work that way in the real world:

[ETA: in the Star Trek example, notice how the right decision for the humans to make is known by looking at the reputation. Where does reputation come from? Right, past actions.]

  1. By “rational”, you really mean “rationally self-interested”. While your real-world (well, really fake world) situation doesn’t really differ in the self-interest department, the real world does.

  2. In realpolitik, the goal is power (or security, which you obtain through power). Power is inherently relative — hence, one actor increasing its power by definition decreases the power of all other actors. Hence, the particular game you describe does not apply well (at all?) to the field of politics.

10

But the fact that we feel such satisfaction is the irrational part. An emotional reaction that most likely evolved because people who walk away from such insultingly bad offers tend to get better ones instead.

11

To be fair, you could make a decent argument that, if one’s feelings are the good to which one works, then in fact, the “irrational” choice is rational inasmuch as it works best toward the good. I suspect that argument is in an important sense true, but it also takes the definition of rationality a bit too seriously.

Incidentally, there was a piece online… somewhere… a while ago. Maybe they linked to it here on the SDMB. Anyway, the gist of the game was that the two players bids a price between $.01 and 1.00. The player with the lower bid gets the amount that he bid*, while the player with the higher bid gets bupkis. Game theory would demand that the rational player bid .01. But a player who bids more than $.01 will tend to do much better. Hence, the irrational player comes out better. And you don’t need to add in knowledge of the other player for this result to occur.

*Or was it the sum of the two bids? Any help? The game is more meaningful the first way, since it strongly resembles real-world situations.

12

This is one of the arguments I refered to, which economists use to try to save their definiton of rationality. They add in the concept of utility and argue, for example, that declining an offer of one cent gives you a feeling of satisfaction with a utility value equivalent to five cents. So the five cent utility value is higher than the one cent actual value. Or a person that makes a 50/50 offer might feel a sense of charity with a utility value equivalent to five dollars. So he made the rational choice of choosing the higher valued 50/50 offer (five dollars in cash plus five “dollars” in feeling good) over the maximim/minimum offer ($9.99 in cash).

But I think these are unneeded complications. The original set-up of the game was supposed to be based on getting as much money as possible. Introducing the concept of utility changes the rules after the fact. And, as I said, it’s unnecessary. No utility needs to be added to rationalize the outcome: the cash value of the supposedly irrational divisions is higher than the cash value of the theoretically rational ones. People are achieving the rational goal, they’re just doing it by what apparently should be an irrational means.

13

I’m not sure what your point is here. Isn’t the ultimatum game the same as the realpolitick you’re describing? One person’s gain is achieved by another person’s loss.

14

No, there is nothing irrational about feeling pleasure. I could just as easily say that seeking to acquire a lump of shiny metal is irrational.

Ultimately anything humans do for any reason is irrational. We’re all gonna die and eventually the universe is gonna cease to exist. All our works truly are vanity.

All any individual can do is decide what there personal goal is and work towards that. If your personal goal is the acquisition of wealth then taking the penny might make sense. If your personal goal is the pursuit of happiness than not taking the penny makes sense. If your gaol is to pursue justice then you want to reject the penny. If your goal is to help others then you want to accept it.

But the point to realise is that none of those goals is rational. Not one. Any one is arbitrary and irrational. It is no more irrational to feel pleasure at evening the odds than it is to dispassionately seek to acquire wealth.

In short, there isn’t some ultimate standard of rationality any more than there is an ultimate standard of justice or morality. Any standard by which to measure rationality is arbitrarily imposed by a human being. These studies often start with the premise that rationality demands that a human being seeks to maximise wealth. But that premise isn’t just irrational, it’s demonstrably incorrect.

15

But were they the rules? Were the players really told that their goal was to “get as much money as possible”?

Because if they weren’t told that, then that wasn’t the basis of the game at all. It is an unwarranted assumption on the part of the researchers.

And if they were told that, then all this demonstrates is that people are capable of cheating. Anybody who isn’t severely mentally retarded knows that “anything” is greater than “nothing”. So every player knew that, in order to follow the rules they had been given, they had to accept the offer. IOW the players who rejected the offer were deliberately breaking the rules for their own benefit, ie cheating.

IMO the whole premise of trial is fundamentally flawed if you are arguing that the basis is getting as much money as possible.

16

My point was that context matters. In the field of international relations (or interplanetary relations, as it were), rationality hinges on whether we make liberal or realist assumptions. Liberals assume that absolute gains are what matter; realists assume that security matters. In a liberal world, the other actor gets a lot, but you still get a little bit, and that’s better than both of you getting nothing. In a realist world, you get a little bit, but the other guy gets a lot, and because his wellbeing threatens your own, that’s worse than both of you getting nothing.

Does that make sense?

Ah, but I do see that I was thinking more about the second actor’s choice (since that is what you talked about most), and you’re thinking more about the first. Sorry for the mixup. But ultimately, the first actor is trying to get the best deal for himself, meaning the worst deal he can convince the second actor to take. In that case, if a rational second actor is assumed, we still need to know the context. If a rational second actor isn’t assumed, then the first actor would need to know something about the second in order to justify a suboptimal decision, right? So if we assume no knowledge of the other actor…

I’m not sure I see the problem. I’ll come back to this after some sleep.

17

There are many reasons listed in this thread that show how Game Theory is too simplistic for ‘real world’ situations. As an analogue, consider the Monty Hall problem and how the statistical solution differs from the situation in the actual game show. Good strategists try to determine the crucial behavioral factors governing their ‘opponents’, and choose ‘game’ strategies to match. Another example is Poker. If you simply play the odds, skilled players will take you apart. Pure rational play by the definition of the OP would result in all players coming out even in the end (not exactly in the real world because you can’t play forever, and not everyone plays the odds perfectly). If you want to really look at irrationality, consider people who play the slots at casinos and buying lottery tickets. Someone remarked that this should not be considered gambling, because you never win. Almost all slot players either play a few games and give up having lost a small amount, or play until they have exhausted their stake and anything won along the way. A lucky few do win a huge jackpot, but the rest go through alternating periods of complaining about the waste of money and justifying the expense as entertainment. Then they go back to the casino to do it again. Lottery tickets are most irrational since each ticket increases your odds of winning by smaller amounts than can be justified from a statistical win. In many of the state lotteries, you would lose money by buying every ticket, even in cumulative jackpots (maybe all of them now). But we know someone may win, but only if they buy a ticket.

Murray the Cop: There’s only one sport I bet on, (pause), Professional Wrestling!

18

You guys are trying to explain the irrationality rather than see that the irrationality doesn’t exist. You’re trying to explain why these players acted irrationally instead of rationally. But the actual results say they were acting rationally - their actions achieved the goal that a rational person would want to achieve. So judged by the outcome, their actions were rational.

Here’s an analogy: suppose I somehow find out that if I stick my left thumb in my right ear when I wake up in the morning, I’ll make a hundred dollars by some means during the coarse of the day. I’ve tested this and found it’s consistent. On days that I do it, I always make a hundred dollars. On days when I don’t, I don’t make a hundred dollars.

Now obviously I cannot come up with any rational explanation for why sticking my thumb in my ear would cause me to make a hundred dollars. So what should I rationally do at this point?

Stick my left thumb in my right ear every morning when I wake up.

Sure, the idea is irrational. But once I’ve established that it works, the rational thing to do is to use it to my advantage. Doing something irrational is the rational course of action.

19

I’d call it empirical rather than irrational. Isaac Newton didn’t know anything about photons, but that didn’t keep him from making measurements and observations based on the spectrum or improving on telescope design.

20

The amount in the pot really does matter, because not only is it the amount of a ‘reward’ for striking a deal, it is the ‘cost’ of failure for not striking a deal. The ‘cost’ part can be said to be irrational, because neither player will end up poorer than when they started, regardless of how the game plays out. But failing to make a deal is also a lost opportunity to gain more wealth, and I’ trying and failing to find a term to describe this other than ‘cost’.

Likewise, the amount of the cut for Player B really does matter. A one penny gain is no gain at all in a practical sense, because there is virtually nothing that one penny can purchase that will be of benefit to Player B.

I would say that a $10 pot is useless for learning anything significant about human psychology, when played in the developed world, because it is too low an amount for either player to be seriously invested in the outcome. I think it might be interesting to see if the results differ for, say, Somalian refugees, for whom $10 would be a healthy chunck of their annual income.

If you raise the pot up to an amount that equals your monthly or annual income, I bet you would see a change in the game. I think you would see the player As offering a 50/50 split far more often, to assure themselves a significant chunk of change.