A Mathematical Proof that Nice Guys Finish First

Posted on 1st February 2006 by Ryan Somma in Ionian Enchantment

“Subvert the Dominant Paradigm.” – Bumpersticker

Pessimists are forever pushing the “Nice Guys Finish Last” meme on us. People who exhibit selfish behaviors such as cheating and taking advantage of others use this affirmation as a sort of justification for their actions. If they played by the rules, they argue, they would be less successful.

Religionists use this meme to stress the importance of their various faiths. Without religious dogma, they argue, there is no reason for human beings to act in an altruistic manner toward one another. According to this reasoning, altruism does not make sense outside of a religious context.

This meme has taken significant mindshare in our culture, evidenced in the fact that so many people consider it “commonsense.” Unquestioningly we accept that it is our basic human nature to take unfair advantage of one another. Altruistic behaviors are denigrated with characterizations such as “naivety” and labels like “sucker,” warnings that kindness and fair play are not standards for emulation.

But is this “commonsense” valid? Secular Humanists recognize the flaw in such reasoning immediately. Society, the collective cooperative efforts of individual human beings, could never have evolved out of a species whose natural instincts are to lie, cheat, and otherwise betray one another for personal gain.

Such a simple and straightforward reasoning does not work for most people. Either because they do not accept evolution, or are historically ignorant, or cannot see the endless expressions of altruism in their fellow humans, these individuals cannot alter their cognitive schemas to accept what others find apparent through observation (Consider Dr. David Brin’s “Fecundity of Chaos“).

In his book, “The Selfish Gene,” Richard Dawkins has a chapter titled “Nice Guys Finish First,” where he explains mathematically why natural selection rewards cooperative behaviors within a species. He does this using Game Theory research and more generalized version of the classic “Prisoner’s Dilemma.”

In this scenario, two individuals meet, each with two options for reacting to the other, cooperate or defect, producing four possible outcomes. They may both cooperate, or they may both try to take advantage of one another (both defect), or one may cooperate while the other defects.

Players score each round like so:

Scenario A’s Score B’s Score
Both Cooperate 3 3
A Defects, B Cooperates 5 0
A Cooperates, B Defects 0 5
A Defects, B Defects 1 1

Competing Strategies

(AC) Always Cooperate (Very Nice): This strategy will cooperate each round, no matter how many times it is betrayed.

(TFT) Tit-for-Tat (Balanced Nice): This strategy will cooperate the first time and then respond in the exact same manner as the other player did the previous round. If the other player defects, TFT will defect the next round. If the other player cooperates, TFT will cooperate.

(AD) Always Defect (Very Nasty): This strategy will always defect each round.

Pitting each strategy against the other for 10 iterations of the game results in all of the above strategies losing to AD, the most selfish of all strategies. AC, the nicest strategy, loses to AD (0-50). Of the nice strategies, TFT does the best against AD (9-14), but still loses. AD versus AD breaks even (10-10).

  AC TFT AD
AC - - 30:30 0:50
TFT 30:30 - - 9:14
AD 50:0 14:9 - -
Totals: 30 39 64

So in one-on-one interactions, AD is the champion, beating out all other strategies, but society is not a one on one endeavor. A One-on-one Versus scenario ignores the cumulative gains each strategy makes in all of its interactions with the other strategies in a society. We must look at our models in terms of populations.

Let’s see what happens if we make add one strategy to make our society four members strong:

  Original
Totals
+1TFT / Total +1AC / Total +1AD / Total
AC 30 +30 / 60 +30 / 60* +0 / 30
TFT 39 +78 / 117* +60 / 99 +9 / 48
AD 64 +14 / 78 +50 / 114 +74 / 138*

*Because there are now two TFTs, ACs, or ADs in the environment, that strategy gets twice the points when encountering each other.

Add 3 Tit-for-Tat strategies to this equation and the rankings change even more dramatically:

1. TFT(173)

2. AC(120)

3. AD(116)

Human beings propagated across the Earth, forming tribes and societies comprised of different combinations of intrasocietal competitive/cooperative strategies.

A Society of 3 ADs: 90 Points

A Society of 3 ACs: 240 Points

A Society of 3 TFTs: 240 Points

A population with a majority cooperative strategies will excel far beyond a population of nasty ones. A cooperative society encountering a nasty society will have a tremendous point advantage, but this could diminish quickly as the Nasty strategies take advantage of the cooperative. For this reason a healthy dosage of judicial strategies are required to keep a Cooperative society safe.

Natural selection will reward the judicious and the altruistic on the level of a single community’s members’ interactions. Communities of altruistic and judicious individuals will be far more successful than societies of cheaters.

These are mathematically demonstrable facts. So the next time a religionist tells us there can be no good behavior without religion, we should ask them if they have a half-hour see our proof.

Further Reading:

I discovered this concept is explained in biology with a mathematical formula known as: Hamilton’s Rule.

Charity Begins at Homo sapiens

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