Joseph Thiebes (thiebes) wrote in clerk_house,
Joseph Thiebes

The Fraternal Dilemma

Updated from an earlier draft from my own LJ, Aug-11-2005 ev.


In the ongoing discussions about local dues, I have at times referred to social dilemmas and game theory. My understanding of these topics is rudimentary. It is plain, however, that social dilemmas are meant to model exactly the kind of cooperative difficulty that the O.T.O. is encountering today in U.S. Lodges. These Lodges must have dedicated space, so called, but they may not require initiates to bear the financial burden of such a space. Initiates in an area where their Lodge has significant expenses therefore face a dilemma: to contribute and volunteer, or not; in either case, they can be initiated and attend initiations so long as they remain active and on good report with U.S.G.L. In many cases they can also attend other events such as the Gnostic Mass without contributing. By analyzing this situation in the light of the study of social dilemmas, we can gain a deeper understanding of the challenges we face as we move out of living rooms, and increase our membership numbers and expenses. To begin, I will describe some of the core concepts of game theory and explain how they can be used to model social dilemmas and local body fund-raising, and I will then provide some brief notes on the common approaches to solving social dilemmas.

What follows is not an attempt to argue in favor of a mandate for local dues; rather, this essay is simply one autodidact's rough stab at modeling the social dilemma we're struggling to overcome, in the hope that it might inspire others to innovate, impart, and implement a variety of means toward our common ends of performing the rituals rightly with joy and beauty; doing things well, and with business way; and promulgating the Law of Thelema through the cultivation of the ideals of individual liberty, self-discipline, self-knowledge, and universal brotherhood. In addition to these aims, I'm certain that some readers can contribute to the model and make it better reflect the complexities that vary by location or personal experience.

Social Dilemmas

A social dilemma is a paradox
wherein the accomplishment of a common goal
requires voluntary cooperation from a group.

Individuals benefit, however,
from the group's accomplishment of the goal
whether or not the individual cooperates.

Yet, if no individuals cooperate
then all individuals will be worse off than they would have been
if all had cooperated.

A public radio station subsists on voluntary contributions; however, all people in the listening area may benefit from the radio station's continued survival, without regard to whether or not they personally contribute. Indeed, many may listen to the station for years without contributing. In this example, raising the radio station's annual funds is the goal to be accomplished, which carries the intrinsic reward of the continued existence of the radio station. Raising these funds requires the voluntary cooperation of donors, but donation is not required to enjoy the radio station. So as long as enough others cooperate by donating, one can continue enjoying the radio station without cost.

Compare this to a Lodge which has significant expenses. At such a Lodge, a goal is to raise the funds needed to pay the bills. Sekhet-Maat Lodge has a quarterly goal of $3900, for example. The intrinsic reward of accomplishing this goal is the continued presence of the Lodge at its current location, the benefits of which have been amply described elsewhere. Accomplishing this goal requires the cooperation of initiates who donate money, and time volunteering to help raise funds through events and other projects. However, anyone may benefit in any number of ways from the presence of the Lodge, whether they contribute or not.

Modeling the Fraternal Dilemma

  • Traps and Fences
    There are two main types of social dilemma—the "social fence" and the "social trap." Local bodies and public radio are of the "social fence" type, wherein a benefit is provided to all while voluntary contributions are made by some (who are said to have "scaled the fence"). In the "social trap," not apparently applicable to local bodies at this stage, a resource is available which people must voluntarily refrain from over-using lest the resource become depleted (as in farmers letting cattle graze on a public pasture). In either case, all participants would be worse off if everyone decided not to cooperate—the radio station lacking contributors would close, and the pasture that is grazed with wild abandon by all farmers would perish.

  • Zero-sum and Non-zero-sum Games
    A zero-sum game has a winner and a loser. We're all familiar with the 0=2 equation—that is, (+1) + (-1) = 0. If you call a winner "+1" and a loser "-1," this formula becomes a clear illustration of a zero-sum game, as the meaning of the phrase "zero sum" is simply "adds to zero." Board games like chess and checkers are zero-sum. A non-zero-sum game is one which, simply, does not add to zero. Whether you have a "win-win" or a "lose-lose," or the winnings are unequal, or the number of players changes the total, the basic idea is that it can add up to a non-zero-sum. Fund-raising at local bodies is clearly non-zero-sum, because all participants receive intangible benefits, whether they contribute or not. We can consider having a space, where we receive such benefits as attending events, taking initiation, magical training and the like as a "win," and the lack of the space to have these opportunities as a "loss." Looking at it this way, you can see that most of the time at Lodges and even most Oases, many initiates and others win, and the "sum" of the wins will be far greater than zero. Naturally some can win more than others by taking better advantage of the opportunities, or win less by bearing more of the cost burden, and some local bodies might offer more or fewer opportunities to their members compared to other local bodies. It is also important to consider what the local initiates value as a "win"—see below for more on these kinds of complexities.

  • Public Goods
    Public goods are resources from which all can benefit, regardless of whether they have helped provide the resource by contributing. As in the example above of a public radio station, the "public good" is the signal being sent over the airwaves. Anyone can tune in, whether or not they donated to the station. Our local bodies generally do not have entirely public goods; that is, we limit much of our activities' attendance to initiates, and sometimes to members of the local body. Looking at specific services provided by local bodies in context, however, there are many which are available to all regardless of contribution. Some local bodies offer most or all of their services without any fee. Most do not charge a fee to attend Mass.

    Local bodies are prohibited from attaching anything more than minuscule fund-raising to initiation, thereby making initiation a public good in essence. The requisite national dues and fees, along with sponsorship and freedom, do not significantly or meaningfully place limits on who can take initiation in this context, since they do not have any affect on the real cost that the local body encounters in providing the service. To explain this last comment further, an example: if your public radio station is on the FM dial, that limits who can listen. Only people with FM radios can listen if you are on the FM dial. Listeners might have to spend more on a radio, but the station is available for anyone to tune into, so it is still a public good even though some may not be able to afford a radio at all. The station derives its income from voluntary contributors. In this illustration, paying the requisite dues and fees, and obtaining sponsors, is comparable to buying a radio. Anyone who does this can benefit from initiation in the Order, regardless whether or not they contribute funds or time to pay the bills that keep the local body alive.

    Social dilemmas always involve a public good. As explained above, a social dilemma is one in which any may benefit from the good, whether or not they cooperate to ensure the ongoing existence of that good.

  • Cooperation and Defection
    Cooperation refers to the individual act of paying some cost (in time or money, for example) or making some sacrifice (like refraining from grazing too much) in order to meet a common goal or provide a common resource. Failing to cooperate is called defection.

    For example in our social fence, a local body might have a dues program intended to cover the majority of its bills. An individual paying local dues would then be "cooperating," while not paying local dues would be "defecting." Or, a local body might have an annual car wash fund raiser for which individuals volunteer to work—in this example, volunteering would be cooperating, while staying home would be defecting. Each time any individual is presented with a choice to cooperate or defect, whatever the specific circumstances, that individual faces the social dilemma.

    In a dilemma involving two people, the possible outcomes can be modeled as follows, with one person's action in BLUE and the other person in RED.

    Cooperate Defect
    Cooperate CC DC
    Defect CD DD

  • Outcome Values and Game Types
    The value that the participants place on the above outcomes will determine what kind of game it is. Here are a couple of the most commonly applicable games in social dilemmas:

    • Prisoner's Dilemma
      Imagine a game where two people exchange envelopes. They can choose to either put 50 cents in the envelope or not, before passing the envelopes to the "bank" where the total money from both envelopes is matched, with the matching funds added evenly to whatever was originally in the envelopes. In this example, placing money in the envelope is "cooperating," while not doing so is "defecting." So, for example, if both players put 50 cents in the envelopes (both cooperate, "CC" above), the bank would see $1, which it would match and add 50 cents to each envelope along with the money already there, so that both players receive a total of $1. If BLUE defects and RED cooperates (DC), the bank sees 50 cents total, matches it, splits it, and puts 25 cents in each envelope—giving a total of 75 cents to BLUE and 25 cents to RED (remember, they are exchanging the envelopes, so the envelope given to RED by BLUE would be empty but for the addition by the bank). If neither player places money in the envelopes (both defect, DD), the bank sees nothing and adds nothing. As you can see, a player doing this would make the most money if he defects while the other cooperates (DC), for in this situation he contributes nothing but receives 75 cents. The next best is for both to cooperate (CC), since that requires contributing 50 cents but each player gets back a dollar. Third best is mutual defection (DD), gaining nothing but also costing nothing. Finally the worst is to cooperate when the other defects (CD), because contributing 50 cents and only getting 25 cents back is a net loss.

      Envelope Game: Prisoner's Dilemma
      Cooperate Defect
      Cooperate Net 50¢
      Net 50¢
      Net -25¢
      Net 75¢
      Defect Net 75¢
      Net -25¢
      Net $0
      Net $0
      DC > CC > DD > CD

    • Assurance Game
      In the Assurance Game, the top two values are reversed from Prisoner's Dilemma, so that mutual cooperation offers a greater benefit than unilateral defection. To use the above example again, imagine that, instead of always matching the amount in the envelopes, the bank gave three times as much when it found a dollar. So, when both people add 50 cents to the envelopes (CC), the bank sees $1 and adds $3, adding $1.50 to the envelopes that already had 50 cents in them, for a total of $2 per player. However, when the bank sees less than a dollar, it matches what it sees as before, so that if BLUE defects and RED cooperates (DC), RED gets 25 cents and BLUE 75 cents as before. Likewise, when both players defect (DD), the bank sees nothing and adds nothing. In this scenario, both players are much better off by mutually cooperating, since the payoff is so much better than unilateral defection or mutual defection. However, in the case of unilateral defection, it is still better to be the one to defect (DC) than the one to cooperate (CD); and mutual defection (DD) is still better than being the sucker (CD). Some may think that this is no dilemma at all, and that cooperation is the only rational choice; however, as implied by the name of the game, mutual cooperation rests largely on the players being assured that the other will cooperate. If there is reason to suspect that the other player will defect, it is best to defect, though similarly the other player is only likely to defect if they suspect you will.

      Envelope Game: Assurance
      Cooperate Defect
      Cooperate Net $2
      Net $2
      Net -25¢
      Net 75¢
      Defect Net 75¢
      Net -25¢
      Net $0
      Net $0
      CC > DC > DD > CD

  • Iteration
    When a game is iterated, it means that the game is played repeatedly. If the players can identify each other and their behaviors can be recorded, players can adopt strategies to, for example, encourage cooperation, or they can manipulate the other player into being a sucker as many times as possible. There are a number of strategies that can be employed, with varying degrees of success depending on the specific rules of the game and the behavior of other players. More on strategies to promote cooperation can be found below.

  • Multiple-person Dilemmas
    Prisoner's Dilemma and Assurance are ideally suited to model two-person games. When multiple people are involved in a social dilemma, it complicates the model geometrically. One easy way to simplify such models is to take it from the perspective of a given individual. Using the same 2x2 chart as above, assign RED to the individual, and BLUE to "everyone else" or even " most others," as follows (note that only RED's outcomes are shown to highlight what each individual considers in facing the dilemma).

    • Example 1
      Soror A.U.M. gets a phone call from one of her O.T.O. brethren. The Lodge is holding a car wash fund-raiser that will bring in money for a badly needed new Mass altar, and they're wondering if she would have time to come and help. She has four potential outcomes to consider:

      Sr. A.U.M. Cooperates Sr. A.U.M. Defects
      Most Others
      Benefit = new altar
      Cost = time spent
      Benefit = new altar
      Cost = 0
      Most Others
      Benefit = 0
      Cost = time spent
      Benefit = 0
      Cost = 0

      Is this an Assurance Game or Prisoner's Dilemma? As you'll recall from above, the type of game depends on which outcome is the highest value to the individual, which is the second most valuable, and so on. This will sometimes vary by the individual. Perhaps Sr. A.U.M. is a Priestess and is tired of that rickety old altar. She likely values the goal highly enough that mutual cooperation is to her the highest value, and it is therefore an Assurance Game to her. She will be likely to show up and help as long as she is assured that a sufficient number of others will also. In a group that is primarily composed of people who routinely see cooperative opportunities as Assurance Games, there is still a dilemma because each person must have assurance in order to cooperate. Assurance can be hard to provide, depending on the specific circumstances.

      On the other hand, if she does not think that the Lodge really needs a new altar all that badly, though she thinks it would be nice, she is likely to conclude (perhaps unconsciously) that the new altar depends more on the actions of everyone else than it does on herself, so there is no need to cooperate. On an individual basis, this conclusion is perfectly rational; if everyone makes this choice, however, it leads to an unfavorable outcome for all—this is the essence of social dilemmas. In this case, the highest value is to get the new altar without contributing time (DC), and is therefore a Prisoner's Dilemma.

    • Example 2
      Soror A.U.M. gets an email from her local body. It's an email that she sees every month which shows the current financial status of the Lodge. At the beginning is a plea for all to take on the mantle of stewardship and contribute $20 per month. She has four potential outcomes to consider:

      Sr. A.U.M. Cooperates Sr. A.U.M. Defects
      Most Others
      Benefit = Lodge has a space
      Cost = $20 per month
      Benefit = Lodge has a space
      Cost = 0
      Most Others
      Benefit = 0
      Cost = $20 per month
      Benefit = 0
      Cost = 0

      What kind of game is this, Prisoner's Dilemma or Assurance?

  • Individual Strategies and Transformations
    If two people sit down to play the Envelope Game repetitively, they will consciously devise strategies to maximize their wealth. One such strategy which works well to promote cooperation is called tit for tat. With this strategy, BLUE would start by cooperating on the first turn, and then mimic RED's action from the previous turn, every turn. If successful, BLUE transforms a Prisoner's Dilemma into an Assurance Game, by effectively promoting mutual cooperation as the highest value, trumping both unilateral and mutual defection. A person might also develop strategies based on the other's behavior, to attempt to manipulate them into cooperating even as we defect, for maximum profit. Such strategies reinforce the Prisoner's Dilemma.

    In multiple-person dilemmas, some players may think they are playing a different game, because they hold different outcomes as the highest values. Someone who does not like the space that a Lodge has rented, and who preferred the living room from yesteryear, may even place mutual defection (DD) as the highest value. More commonly, people will place mutual cooperation and unilateral defection in the top two spots, and either approach the situation as an Assurance Game or Prisoner's Dilemma, sometimes changing their perspective multiple times in the course of a given year.

  • Production Function
    One important trait to examine in social dilemmas is the production function, which is the relationship between the amount contributed and the level of "public good" that is provided. In other words, when contributions increase, how does this affect the benefit gained by the group? There are four basic diagrams that most social dilemmas will fit, depending on the particular situation.

    A decelerating function illustrates a situation where the first contributions do the most good, and as contributions increase, each dollar or hour contributed helps less and less, until the line flattens out at the top.

    A linear function shows that as contributions increase, benefits increase apace.

    An accelerating function reflects that when contributions are small, there is not much benefit, and additional contributions increase the benefit slowly; but over time, the benefits increase faster and faster. After a certain point, the benefits start to outweigh the contributions, and this disparity grows with the contributions.

    A step function or threshold occurs when contributions do not make any difference for a time, until a specified amount is collected, at which time a dramatic shift in benefit occurs.

    Kollock, Peter (1998 EV). Social Dilemmas: The Anatomy of Cooperation.
    Department of Sociology, UCLA. Retrieved August, 2005 EV

    These functions can have a profound effect on the way individuals see the situation and the value of their own contribution. In a decelerating function, early adopters will have a higher incentive to contribute, since their efforts will have the greatest impact. In a linear function, the comparison between contributions and benefits is straight-forward, no matter how much has been raised before. In an accelerating function, it may be more difficult to get started and to attract contributions at first, until benefits begin to outweigh contributions. In a step function, a threshold that seems too far away for any one person's contribution to make a difference may demotivate potential contributors, while a threshold that seems easy to attain will give people the sense that their efforts could put the whole group over the top. Using these models to examine any fund-raising effort will help to understand how others will view the value of their contribution and the benefit they will derive from it.

  • Nash Equilibrium
    Named after John Nash, of whom A Beautiful Mind is a biopic, a Nash Equilibrium occurs when the strategies of all players affect the outcomes such that no player can improve his own benefit by changing strategies. When a Nash Equilibrium is present, it is unlikely that players will change their approach, because doing so does not benefit them. Using the example of the car wash again, let's say it's an annual event, and each year the funds are raised for a different purpose. Sr. A.U.M. has skipped out on these every year for the last five years, and yet the others have met their goal each time. Is she likely to change her strategy this year? No, because doing so will not affect the benefit that will come of the car wash—a benefit that she sees as very probable or even as an inevitability. She might change her strategy if she is concerned that her presence is needed to raise the funds needed, or if she wants very much to meet someone who is going to be there this year, or if she has recently decided to study to be a professional car washer and would like to get the experience. Likewise, Fr. L.U.X., who has worked the car wash every year, is not likely to defect out of the blue unless he thinks that the car wash can go on without him; in which case he can increase his benefit by not attending, since he will still be able to use the mass altar when it is purchased. If all those who cooperate and work on the car wash believe that they are needed, and all those who do not attend believe they are not needed, it is a Nash Equilibrium, because nobody has any incentive to change their strategy.

Strategies to promote cooperation

Motivational Solutions

  • Communication
    • gathering information about what others do has ambiguous effects
      • if you know that many others are contributing to the common goal:
        • in an Assurance Game it can motivate toward cooperation
        • in a Prisoner's Dilemma it can motivate toward defection
      • if you know that few others are contributing:
        • in an Assurance Game it can motivate toward defection
        • in a Prisoner's Dilemma it can motivate toward defection
      • in a decelerating function, there is less incentive to contribute if many others have
      • in a accelerating function, there is more incentive to contribute if many others have
      • in a step function the effect will depend on how close the group is to the threshold:
    • promises to each other may or may not have any effect
    • moral persuasion may have some beneficial effect
  • Group Identity
    • members of a group will be more likely to cooperate with each other than with outsiders
    • applies especially to commons (social traps)
    • inter-group competition dramatically increases effect of group identity

Strategic Solutions

  • Grim Trigger
    • each person cooperates only if all others cooperate
    • high risk of mutual defection, but cooperation is decisive when it occurs
  • Social Learning
    • when participants do not calculate their strategies but operate less cognitively and simply "lean" toward cooperation or defection
    • the presence of thresholds can help cooperation
    • leaders that exemplify can also help cooperation
  • Group Reciprocity
    • group identity is important
    • this is the group version of "tit-for-tat," which requires identifiability of participants and their decisions as well as iterative decision making
    • borne of interdependencies, not arbitrary categorization
    • reciprocity among group members encourages cooperation due to belief in future reciprocity
    • can manifest as a strategy even when reciprocity is not logically possible
    • transforms Prisoner's Dilemma into an Assurance Game

Structural Changes to promote cooperation

  • Iteration and Identifiability
    • required for tit-for-tat and group reciprocity to work well
    • iteration means that the choice to cooperate or defect is encountered repeatedly
    • identifiability means that individual choices are known by all participants, so that reciprocity can occur (at least in theory)
    • even if reciprocity is not logically possible, iteration and identifiability may cause people to behave as though it were
  • Payoff Structure
    • changing the benefits of each type of outcome will change the name of the game
    • if more benefits are available when mutual cooperation occurs, transforms Prisoner's Dilemma to Assurance Game
  • Efficacy
    • changing the situation in such a way that individuals feel their contribution will be more effective
    • pointing out thresholds, or explaining the production function of the current situation can increase the perceived efficacy of individual contributions
  • Group Size
    • as groups grow larger, it becomes more difficult to overcome social dilemmas by any of the above means
    • studies have shown that this effect diminishes quickly, possibly due to critical mass
  • Metering
    • contribution is required for use of a resource, for example charging a fee to attend a class
    • used widely in local bodies, with varying rates of success
  • Heirarchy
    • authority is used to compel individuals to cooperate
    • can imply punishment for defection, thereby changing the values of the outcomes
  • Boundaries
    • a limit is placed on who can access the public good
    • often includes heirarchical or metering aspects
As mentioned in the introduction, it is my hope that the above analysis can help others to understand some of the issues we face. Perhaps in reading this, you will have ideas for how to stimulate cooperation to accomplish common ends at your local body, whether you're taking on the large project of renting 24x7 space, or just trying to hold a communal garage sale. Perhaps after holding a fund-raising event, you will find that referring back to this document might give you ideas about why it turned out the way it did, successful or unsuccessful. Perhaps by looking at the different strategies and values that people assign to different outcomes, you will be able to understand your brethren better when they make different choices than you do.


Tags: diagnosis, game theory
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