Joseph Thiebes (thiebes) wrote in clerk_house,
Joseph Thiebes
thiebes
clerk_house

The Fraternal Dilemma, Part 4

Assurance Strategies

Since I originally wrote Part 2 in this series, two local bodies have employed different tactics in an effort to change the game from Prisoner's Dilemma to an Assurance Game. In an Assurance Game, mutual cooperation is assigned a higher value than unilateral defection. When voluntary contributions provide a public good, it can be difficult to shift the values of the outcomes. Even if the attempt is successful, Assurance Games have their own drawbacks. In this installment I will describe the two strategies, explain how they work and attempt to discover their weaknesses.

  • KTO Membership Meeting

    Knights Templar Oasis held a meeting with their members, with one question to answer: to take on fund-raising as a regular activity, or to divide the costs evenly among the members so that fund-raising is unnecessary? Consensus was quickly reached to divide the costs and bear the financial burden, rather than spend a lot of time and energy plaanning and executing fund-raising events.

    The choice offered to the members transformed the game. OTO is not a fund-raising club, so it can be reasonably presumed that most will not want to do fund-raising activities which have a tendency to preclude other, more relevant, activities. Given this, the idea of mutual cooperation becomes more appealing to most members than unilateral defection, because unilateral defection on anyone's part necessitates fund-raising. In short, for a perceived win, all must contribute; if anyone defects, everyone loses. This was an ingenious method to transform the game, and catapulted KTO to self-sufficiency—making KTO the first local body that I know of to accomplish this feat.

    One interesting facet of KTO's approach is that it is a Grim Trigger, which is to say that it would only work if everyone was on board. If a single member refused, it might be possible to work around, but the principle of the tactic would be compromised by it. Therefore for this game, it is more important to consider whether all cooperate, or any defect, rather than considering the actions of most.

    As you can see in the chart below, if fund-raising activity is considered by many members to be a significant "cost," the choice presented by KTO has a clear favorite outcome. For convenience, I'll assume that any fund-raising effort would be successful in bringing in the necessary income to pay the bills. Obviously, any doubt about the potential success of fund-raising would make mutual cooperation even more attractive.

    Cooperation = paying one's equal share of the expenses
    Defection = only paying minimum
    T = the ability of the local body to pay its bills and continue to exist at its current level of financial responsibility
    NF = no fund-raising effort
    F = fund-raising effort
    Sr. A.U.M. Cooperates Sr. A.U.M. Defects
    ALL Others
    Cooperate
    Benefit = T + NF
    Cost = Dues
    Benefit = T
    Cost = F
    ANY Others
    Defect
    Benefit = T
    Cost = Dues + F
    Benefit = T
    Cost = F

  • The Glass Bead Game

    This tactic was employed at Sekhet-Maat Lodge by an individual (the present author). Rather than divide the costs equally among members, a cup with beads in it was presented, and each person present was asked to draw some number out, each according to their means. Each bead drawn from the cup represented a commitment to contribute $5 more per month. The total number of beads in the cup reflected the monthly shortage that SML was enduring. To drain the cup, therefore, was to eliminate the deficit and reach self-sufficiency. In the presentation of this game, the many benefits of self-sufficiency were brought up, including that self-sufficiency would remove the constant need for fund-raising.

    This did not have the same kind of force that KTO's meeting did, but it did have a certain charm which captured the imaginations of those participating. Rather than presenting the alternatives of fund-raising or reaching self-sufficiency, the latter choice was presented as a goal, with the beads in the cup representing the distance to accomplishing that goal. Because of this difference, the game was not a Grim Trigger. Any progress toward self-sufficiency was presented as a benefit, and the object was to reduce the deficit as much as possible to reduce the necessity of fund-raising.

    As one might suspect, self-sufficiency was not achieved with this game. The deficit was, however, vastly reduced, to the extent that SML's fund-raising efforts have been indefinitely diverted to provide needed improvements rather than simply paying bills.

    One of the interesting features of this game is that it was done blindly; that is, none of the members knew what other members drew from the cup. In a way, this heightened the sense of "assurance," because presumably, the lack of social pressure meant that each person was making a commitment that they were not pressed to make. Thereby, one could reasonably presume that the private commitments that the members made would be kept.

    In the chart below, you'll see that the actions of others can be considered in terms of what most others will do. As mentioned above, this is not a Grim Trigger, so even if some do not participate it can still work.

    Cooperation = taking beads and following through with commitment
    Defection = not taking beads, or not following through with commitment
    T = the ability of the local body to pay its bills and continue to exist at its current level of financial responsibility
    LF = less fund-raising effort
    F = equivalent fund-raising effort
    Dues = minimum dues payment amount to be considered a member in good standing
    Pledge = value of beads drawn by a Soror A.U.M.
    Sr. A.U.M. Cooperates Sr. A.U.M. Defects
    Most Others
    Cooperate
    Benefit = T + LF
    Cost = Dues + Pledge
    Benefit = T + LF
    Cost = Dues
    Most Others
    Defect
    Benefit = T
    Cost = Dues + Pledge + F
    Benefit = T
    Cost = Dues + F

    Anyone following along may look at the above chart and wonder: doesn't this show a Prisoner's dilemma? Well, yes it does. Note however that "LF" is a variable benefit, which improves with the number of people cooperating. Also, the way the game was presented made it unlikely for anyone to choose to take no beads. Since most (if not all) would take beads, and given the extreme benefit of lessening fund-raising necessity to zero, members were likely to consider carefully what they could afford.

Reassurance

The most prevalent difficulty in an Assurance Game is providing assurance. How do the participants know that others will cooperate? Once trust is established, what will happen if anyone defects later?

In a Grim Trigger like KTO's approach, a single defection can kill any prospect for the success of the game. Yet, if mutual cooperation is achieved at first, that outcome will tend to be decisive and lasting. The question is: how long will it last? If, for example, one member loses their job a year later, will others pick up the slack? It seems likely they would. What if, on the other hand, two members simply decide to stop contributing their share at some later time? This might have deleterious effects; others may decide that the "equal share" has gone up too much, or they may become demoralized. If someone did defect, notifying members of the defection and the resulting increase in the "equal share" might require careful handling.

The Glass Bead Game, as mentioned before, attempts to build some assurance by making it easy for each participant to make a choice based on their means. Since each person made a private determination about what they could contribute above the baseline dues amount, there was a high degree of confidence that each participant would be able to meet that commitment. On the other hand, because each person made a private choice, it would be very easy for anyone to back out. In the end, the reality of our income over the following few months was such that we were able to cease fund-raising efforts directed at covering expenses.

Equilibrium

Both of these approaches attempt to achieve self-sufficiency. What happens when that goal is attained? Will new members be motivated to contribute, knowing that their predecessors have kept the place up and running for years? Will existing members wish to decrease their contributions when income begins to grow larger than expenses? In an Assurance Game where the goal is to pay expenses, there will be difficulty in going beyond that goal to achieve more robust financial health.

Tags: diagnosis, game theory, solutions
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