Twilight of a Dilemma: A Réplique

Abstract

In light of the nine open peer commentaries, we further explicate the social projection model and highlight its boundaries. We acknowledge that our model—like any extant model—cannot account for all the available empirical data. Yet the model is strong because it explains cooperation in a variety of social dilemmas and experimental games while deploying only one psychological construct as a parameter. Compared with its competitors, the social projection model more openly recognizes the struggle with uncertainty a person caught in a social dilemma must confront. In a series of simulations (and brute math), we show that cooperation can survive when players (humans) stay the Bayesian course.

Acknowledgments

We thank Andra Geana for suggestions on the simulations and mathematical appendices. She took us to a higher place so that we could see farther.

Notes

A literary device denoting a (usually sinister) double of a living person.

Colman has also suggested that coordination games can be solved by common sense and team reasoning (but not by social preference). Once common sense is invoked, how can team reasoning distinguish itself?

Before moving through the innings, we already suspect that the ST will beat social projection because the latter is included in the former. If social projection is excluded, the ST looks very similar to van Lange's social value model, which already includes self-interest.

Kerr adds and subtracts full and half points along the way, so we do the same, although it is a practice that baseballers might frown upon.

We should also note that a significant correlation by itself is weak evidence for a common cause. The common cause may be so remote that it is of little interest as a mechanism. For example, the median age of people in the developed world has been correlated with a rise in average global temperatures and the price of milk. What is the common mechanism? In contrast, the social projection model specifies proximal mechanism.

This is another example for the desirability of individual differences. Without them, these correlations would be undefined.

High projectors do well if group selection is allowed. If intergroup dilemmas are superimposed on interpersonal dilemmas, as in war, the group that mobilizes the most cooperators will prevail over groups whose members defect from one another (Krueger, 2007).

If two players always agree, we want the true value of p_r =1, which means the mean value, . This is only accomplished if every value of λ = 1. This is why an agreement is coded as a 1 and a disagreement is coded as a 0.

A uniform distribution is a special case of the beta distribution (with a = 1 and b = 1), so Laplacian ignorance is preserved. Being the conjugate prior for the binomial, the beta prior makes analytical solutions for Equation 2 possible (see Appendix D for details).

We follow Russell (see epigraph) in our conception of rationality, and we apply the same criterion to our research participants. Individuals engaging in evidential reasoning respect the nature of uncertainty; individuals thinking along moral lines tend not to.