Counterfactual Crusoe

Defoe could have written a less interesting novel.

Posted Jun 26, 2020

 J. Krueger
Weighing anchor for the Island of Despair.
Source: J. Krueger

"I myself exist only insofar as I escape from myself to join with others." –Robinson Crusoe, having a solipsistic moment, as told by Tournier (1969)

"Thank God, it's Friday!" –Crusoe exclaiming when finding he was no longer alone (unauthenticated)

At a time when social isolation has become a reality for many, a second reading of Defoe’s (1998/1791) Robinson Crusoe is profitable. In an earlier essay, I discussed how Crusoe found happiness and how he thought his way through moral dilemmas (Krueger, 2014a). Then, I explored Crusoe’s relationship to Friday as a power game (Krueger, 2014b), concluding that Crusoe and Friday found a mutually beneficial compromise in a situation, in which strict rationality would have derailed them (Krueger, 2014c). In this essay, I want to shed a bit more light on their power dilemma by asking how things could have gone wrong.

 J. Krueger
The original power game.
Source: J. Krueger

Let me first summarize what the dilemma looks like in its original form. Matrix 1 shows Crusoe and Friday respectively as the row and the column player. Each chooses between conciliation (i.e., cooperation) and aggression (i.e., defection). Crusoe’s and Friday’s preferences are shown respectively to the left and to the right of the comma within each of the four cells resulting from the crossing of their strategies. Both would like the other to be conciliatory, but they differ in how they respond to each other. Crusoe plays tit-for-tat, that is, he is conciliatory with a conciliatory Friday, and aggressive to an aggressive one. In contrast, Friday challenges a conciliatory Crusoe, but submits to an aggressive one.

The game-theoretic outlook is rather bleak if each player has a chance to respond to the other. As for each combination of strategies, one player has an incentive to switch strategy, Crusoe and Friday end up going around the matrix in counterclockwise fashion, earning an average preference value of a mere 2.5 and missing the psychological benefit of a stable situation. As Defoe tells it, however, Crusoe and Friday settle into a state of mutual conciliation, where Crusoe realizes his first preference and Friday his second (see top-left cell in Matrix 1). Theoretically, this is not a stable state because Friday has an incentive to rebel, which would let him do better in the short term. Since he does not rebel, we might credit him with foresight and the wisdom to use it.

My decision to let Crusoe be the row player with a taste for tit-for-tat and Friday be the column player with a taste for contrariness may be questioned. If the players were switched, Friday would have the better deal. Is my decision to favor Crusoe an instance of Eurocentric bias? Perhaps. Whatever the case may be, my goal is to model the interpersonal power dilemma described by Defoe using the information provided in the novel. In that novel, a power differential is described as persisting, allowing Crusoe to lead the team. Literature is, of course, fiction, and so it is a small wonder that alternative versions of the story have found authors to write them. Tournier (1969), also a European, tells of a different island, where Friday’s "uncivilized" approach prevails and yields greater happiness, even for Crusoe.

 J. Krueger
Matrix 2. Aggressive Crusoe.
Source: J. Krueger

If we were to treat Defoe’s story as fact, then Tournier’s would be a counterfact. A counterfactual is an alternative to what is, and its contemplation can yield insights into the nature of fact (Byrne, 2016). I now want to use counterfactual settings of the power game and to explore their implications. Consider first the case of a ruthlessly domineering Crusoe. His preferences, as shown in Matrix 2, have changed such his first preference (4) is now mutual aggression and his third (2) is mutual conciliation. Crusoe no longer plays tit-for-tat, although it is still true that he prefers mutual conciliation over unilateral conciliation, and mutual aggression over unilateral aggression. Friday’s preferences are not changed from the original settings in Matrix 1. Aggression is now Crusoe’s dominating strategy, and the best Friday can do is to settle for mutual conciliation. Notice that compared with the original game, only Crusoe does worse. In other words, Crusoe would not want to have these preferences.

 J. Krueger
Matrix 3. Aggressive Friday.
Source: J. Krueger

Next, consider an aggressive Friday. The preferences shown in Matrix 3 are obtained by using Crusoe’s original ranking (as seen in Matrix 1) and by making aggression the dominating strategy for Friday. This is accomplished by making mutual aggression his second preferred outcome (3). Friday still prefers mutual conciliation (2) over unilateral conciliation (1). Knowing that Friday will rebel, Crusoe will aggress, yielding a low outcome for Crusoe himself (2), and delivering the second-best outcome to Friday (3). Here, mutual aggression is a Nash equilibrium, that is, neither player has an incentive to switch strategy. Friday, however, is left with a meta-strategic question: does he prefer the game constituted by his own belligerence (Matrix 3) to the original power game (Matrix 1)? In both games he gets his second-highest preference, but in the former, he does relatively better than Crusoe, whereas he does relatively worse in the latter. Also, going beyond the given numerical preferences, we may note Friday (as many humans) might prefer a state of mutual cooperation over a state of competition and strife.

 J. Krueger
Matrix 4. Docile Friday.
Source: J. Krueger

Finally, consider a perfectly conciliatory Friday. The preferences shown in Matrix 4 are obtained by aligning Friday’s preferences with Crusoe’s. This may look as if Crusoe gets his way, having an island mate who likes what he likes and hates what he hates. Friday, not Crusoe, has a dominating strategy. He will conciliate. Crusoe will respond with conciliation, leaving both in an efficient Nash equilibrium state. One might object that this variant of the game projects a false harmony, obtained with the process by which the matrix was set up. Recall that the first assumption was that Crusoe prefers a gentle Friday. The matrix was then filled in to grant this wish. Useful as it is, the theory of moves (i.e., the heterodox variant of game theory used here) allows the modeling of interpersonal relations and dilemmas. Much depends, however, on how the preferences are estimated and established by the researcher or the involved parties themselves (if they are around to be asked). Comparisons between different games—as we attempted here by referring to meta-strategies—provide opportunities to bring together game-theoretical analysis and counterfactual thinking.

Defoe and his Crusoe have produced mountains of research and opinion. The Wikipedia page on Robinson Crusoe linked above provides an excellent introduction. Of special interest is James Joyce's (1912) lecture on Defoe, which is linked within this site. Joyce has much to say about Defoe, the Englishman, and what is English and imperial(istic) about Crusoe. Whatever you may think of Joyce's argument, reading his prose is delightful.

References

Byrne, R. M. (2016). Counterfactual thought: From conditional reasoning to moral judgment. Annual Review of Psychology, 67(1),135–157. doi:10.1146/annurev-psych-122414-033249

Defoe, D. (1998/1791). Robinson Crusoe. Mineola, NY: Dover.

Krueger, J. I. (2014a). Robinson Crusoe, psychologist. Psychology Today Online (January 31). https://www.psychologytoday.com/intl/blog/one-among-many/201401/robinson-crusoe-psychologist?amp

Krueger, J. I. (2014b). How Robinson Crusoe managed his man Friday. Psychology Today Online (February 9). https://www.psychologytoday.com/intl/blog/one-among-many/201402/how-robinson-crusoe-managed-his-man-friday

Krueger, J. I. (2014c). A general power game. Psychology Today Online (February 13). https://www.psychologytoday.com/intl/blog/one-among-many/201402/general-power-game

Tournier, M. (1969). Friday. Transl. by N. Denny. New York, NY: Pantheon. Originally published in French, 1967.