Irrationality and Fairness
The Ultimatum Game is a demonstration of either human irrationality or an inherent desire for “fairness.” While I would like to believe that, were I the responder, I would choose rationally to accept any non-zero sum offered, I don’t think that would be the case. In thinking about my choice, I would undoubtedly take into account both the total amount being divided, and the percentage of that payout that would be mine. Given a substantially large payout, I would more likely be willing to accept a smaller percentage - to a point.
For example, if the total payout was one million dollars, and I was only offered 1% ($10,000) - I believe that I would still accept it. But if offered 1% of $100 ($1) - I don’t know that I would. Perhaps I’m taking into account the time required to reach a decision, and my per-unit-time compensation - but it always comes back to a punishment for the offer. It’s also possible that in rejecting the offer, I’m attempting to establish a negative reinforcement against future similar offers, in spite of the game’s stated condition that no such future offer will be forthcoming. Thinking purely selfishly, it is in my best interest (as the responder) to accept any non-zero sum - but if the proposer can count on the fact that I think purely rationally (and selfishly), then it is in his best interest to propose any offer that grants me a non-zero payout, thus maximizing his return. In punishing the proposer for an “unfairly” low offer, I am in effect discouraging the profit-maximization available to the proposer on the purely hypothetical future iterations of the game.
On the other hand, if I were cast in the role of the proposer, my offer would be a 50/50 split. While I could achieve a better result for myself by skewing the offer more in my favor, there is something in my psychological makeup that discourages it. Perhaps it’s my desire to be perceived as fair and impartial, or a conscious or subconscious attempt to “be liked” - but I would have great moral difficulty offering anything other than an even 50/50 split.
(from kottke.org)
April 15th, 2007 at 10:33 pm
The reasoning that makes 1% of $1M appear “better” than 1% of $100, even though the game is played purely with percentages (or ratios) and not real figures, is the same reasoning that is behind a “progressive” tax strategy. Some people perceive that paying 35% of your income is “fair” when the payees are in the top brackets, but it’s still 35% (as opposed to very low to even negative percentages in the bottom 2 full brackets). The reality is, as you mentioned, any non-zero ratio is going to better your position to take it presuming, as the game does, that there are no strings and no chance for reciprocity of any kind.
Presuming the data is available, any good Marxist, when considering the real amount involved (total) and/or the impact that the amount makes on the person offering the money (rich v. poor), would take no less than 100%. Why not? After all, if it’s a Bill Gates type of wealth that is “only” offering a portion of $1M then why not hold out for all of it? After all, $1M is relatively nothing in his case (
April 18th, 2007 at 8:17 am
I disagree with your analogy to the tax system. The principle illuminated by the Ultimatum Game is that people will choose to screw themselves in order to punish someone else. The system of progressive taxation is more appropriately distilled as “screw the other guy in order to make my life better.” The only way you can relate the two is by presenting evidence that both
The only way for both statements to be true is if lower-income welfare vs. government spending isn’t a monotonically increasing function (which is unlikely but debatable) AND if we happen to be at a local maximum of that function at our current level of taxation. (For it to be true in the general case, we would have to be at a local maximum for any arbitrary level of taxation, which is impossible.)
There’s also the point that progressive taxation is implemented in an arguably “fair” fashion - those in the 35% tax bracket don’t pay 35% on their total income, but 35% of their income above a certain predefined threshold, with their income before that threshold being taxed at the lower rates of the lower brackets. Couple that with the general belief that utility gained from increasing income has diminishing marginal returns (i.e. getting $5 when you only have $5 is significantly more meaningful than if you have $5 million), and the reasoning that a large percentage of lower-income individuals earnings go towards basic necessities (while higher income individuals “surplus” earnings go towards luxury items or increasing wealth), and the progressive tax makes a modicum of sense.
A flat tax (which seems to be what you are suggesting) is inherently regressive, forcing the bulk of the burden on those of lower income, while reducing the burden of those most able to pay. Consider an example situation where a group of individuals must move rocks from point A to point B. The rocks must be moved, or the whole community will disintegrate. Why is it unfair that the strongest and hardiest individuals carry the heavier rocks? Is it more “fair” that those least able to contribute (the young, the old, or the sick) be forced to contribute equally?
I’ll also note that the Fair Tax (which I believe you endorse) is inherently progressive. The tax rebate for basic living expenses eliminates the regressiveness typically associated with sales tax, and that same tax rebate (while universally applied) is significantly less meaningful to those at the highest incomes, thus taxing their income at a significantly higher rate than those at lower income.
I also disagree that “any good Marxist” will insist on receiving 100% of the reward - at least not theoretical Marxism. The basic thesis of Marxism is that all individuals deserve an equal share of resources - thus a true Marxist would insist on at least 50%, and a dyed-in-the-wool Marxist should refuse anything greater than 50%, as it would be an unequal distribution. In practice, however, most people will choose the more selfish route and accept anything over the minimum 50%.
Going back to the original game - assuming that the roles are determined completely randomly and each player chooses a strategy from either the rational homo economicus or the Marxist model and those choices are made available to the other player, the results are interesting. Assuming that both players follow the homo economicus model - then the accepter will always be given the smallest non-zero division of the reward, with the proposer gaining the remainder. Any other division (where at least one player follows the Marxist model), the division is always a 50/50 split. If the goal of the game is to efficiently and equitably distribute resources (assuming no prior probabilities), the Marxist model proves far more effective.
It’s only when one factors in some prior probability in terms of role selection that the homo economicus model becomes defensible. In terms of an evolutionary standpoint, the resources are best distributed so that the player with the highest survivability receives the highest payoff - and it stands to reason (at least based on your examples) that the player with the highest survivability is preselected as the proposer. For example, two stone age hunters have an option of hunting a boar. The better hunter makes the proposal to the lesser hunter on the knowledge that he cannot successfully complete the hunt alone. In return, he offers the lesser hunter a portion of the spoils. The lesser hunter is likewise incapable of hunting the boar successfully, so if he refuses the offer, both hunters starve. The better hunter will offer the smallest portion that will allow the lesser hunter to continue living and assisting on boar hunts - and the lesser hunter will always accept. If the better hunter offers any less, the lesser hunter will refuse (he’ll starve either way) and both starve. If the better hunter offers any more, then he is sacrificing his own long term viability for no benefit.
To extend the parable to the modern era - society is a necessity for the accumulation of wealth. Bill Gates’ money didn’t come out of thin air, it was garnered from consumers of his products. In order to continue doing business, Bill needs the benefits of law (to protect his accumulated assets from looting) and a consuming public. As such, he offers some portion of his income as taxes or charity to improve the welfare of those less well off. If he offers less than some minimum amount, the consumer public will revolt, society will collapse, and the strongest among them will seize his assets.