Tag Archives: game theory

Free Will and God

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I am both a scientist and a Christian.  Many people—from both camps—sometimes see these two disciplines as fundamentally incompatible, but I adamantly disagree.  This post explores one question that has troubled me in my Christian walk and may have troubled you:  can free will and predestination both be true? I don’t even begin to claim I’ve solved this riddle, but I describe one way in which both concepts co-exist.

My argument consists of three points.

Point 1 — We all played Tic-Tac-Toe as kids.  At first, it was a lot of fun, but then we tired of it and quit.  Why?  Because sooner or later, we realized that the first player has a big advantage, and then the sport is gone.  Wikipedia’s article describes a strategy for the playing the game of Tic-Tac-Toe where the first player is guaranteed to either win or draw.  Playing this winning strategy ensures the first player NEVER looses. (There is no strategy for the game of Tic-Tac-Toe that ensures a player always wins, but such games exist.)

Now, no one would argue the first player can control or over-ride the second player’s free will.  But still the first player can force (predestine) a win or a draw.  That is, when the first player plays the strategy, he has partial predestination of the outcome; he can “predestine” some important elements of the outcome (e.g. winning vs. loosing), even if it can’t “predestine” every detail (e.g. the second player’s exact sequence of moves).  Both free will and predetermination happily co-exist in Tic-Tac-Toe.

Tic-Tac-Toe is a very simple game.  What about other games?  We simply don’t know whether the exists a winning strategy for either player in chess.  The state space for chess is monumentally too large for a brute force analysis, and no one has produced any other evidence a winning strategy does, or does not, exist.  We simply don’t know. But “maybe”.

Another example is the “Game of the Universe” (GOTU) —our life in this physical universe—which is infinitely more complicated than chess.  Rather than chess’s discrete state space and set of moves, the state space and possible moves for GOTU are continuous and therefore (doubly) infinitely larger (at least aleph-1).  If we can’t figure out whether a winning strategy exists for chess, what chance do we have of figuring out whether there exists a winning strategy for GOTU.  Again, we simply don’t know.  But “maybe”.

So my first point is (1) some games have winning strategies where one player can force play to his desires, and (2) while we have no evidence GOTU has a winning strategy, we don’t have any evidence such a strategy does NOT exists.  All we can say it is conceivable a winning strategy exists.

Point 2 — In a completely different kind of game, there are 5 reasonable properties we desire from a voting system (non-dictatorship, unrestricted domain, independence of irrelevant alternatives, positive association of social and individual values, and non-imposition).  We are reasonable and right to seek voting systems that satisfy all 5 criteria.  But Arrow Impossibility Theorem showed that it is not LOGICALLY possible to have such a system.

So, my second point is, even though we may desperately DESIRE (even demand?) a set of properties hold about a system (here, GOTU), it is POSSIBLE that those properties are logically incompatible.  So we should be careful about our wishes/demands.

Point 3 — All I’ve done so far, is to illustrate that (1) predestination (winning strategies) and free will can co-exist (Tic-Tac-Toe), and (2) it is not always possible to construct systems that have all the properties we desire they have (voting systems).

What does this all mean?  It means God COULD have constructed our world to include both predestination and free will.  It may strike some readers, that it is horribly “unfair” for God to create the world (GOTU) in such a way that he always “wins”.  And some readers may complain that it is “unfair” that our free will does not give us the freedom to alter the final state of the world.  In short, some people may question how can God be so “unfair”.

My only answers are (1) if we don’t know whether or not the game of chess has a winning strategy, how can we make demands on God about whether or not the GOTU should allow a winning strategy.  Plus, it would be ridiculous to made demands that are not even logically consistent.  But God gives His own best answer to an accusation that He might be “unfair” regarding these matters:

Where were you when I laid the earth’s foundation?   Job 38:4

So, I encourage you to exercise your partial free, knowing that the overall end of the world can turn out exactly as God desires it (partial predestination).

Evolutionary Game Theory and the Role of Third-Party Punishment in Human Cultures

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Yesterday I went to a very interesting lecture at Duke University by Professor Dana Nau on Evolutionary Game Theory and the Role of Third-Party Punishment in Human Cultures.

They use evolutionary game theory to help explain the phenomenon of responsible third-party punishment (3PP).  Assume agent A harms agent B.  Then agent C is a responsible third-party punisher (of A) if C spends some its own resources to punish A, receiving no benefit to itself.  Using simulation and a lot of details I don’t consider here, they show that high strength-of-ties and low mobility foster the evolution of responsible 3PP.

While this work considers human cultures, it likely has application to systems of autonomous agents.   And, in particular, how punishment could or should work when agents violate their commitments (commitments are a major element of my own research, which I’ll explain it upcoming posts).

In addition to the meat of this paper, I was particularly interested in the social graph that defines each agent’s neighborhood.  As their approach is evolutionary, they “mutate” (among other things) the social graph during the simulation.  They randomly pick two agents and swap them (I’ll call this “stranger swap”).  This is like ripping these two agents out of their current groups and jamming them into completely different groups.   Each agent adopt the other’s friendships.  This is like Star Trek’s tele-portation, or perhaps The Prince and the Pauper.  This is radical.  Agents can move arbitrarily far, but they can be thrust into neighborhoods of the social graph which have little or nothing in common with their old neighborhoods.

A less radical mutation would be “friend swap” which can swap two agents only if they are currently friends (socially adjacent).  This kind of swap moves an agent to a similar neighborhood.  This is more like slow animal migration than tele-portation.  Of course, since agents can only migrate one step per mutation, it will take longer for them to move as far as “stranger swapping”, but it does a better job at incrementally changing agent’s neighborhoods.  A “friend of a friend swap” would be a middle ground between “stranger swap” and “friend swap”.

All three of these social graph mutations leave the structure of the graph absolutely fixed.  I also wondered about a different kind of mutation which seems closer to what happens in real life.  What about the social mutations of “drop friend” where an agent randomly deletes the relationship (edge) with one of its current friends, and “add friend” where an agent randomly adds a relationship with some new agent.  This means the agent maintains most of its existing relationships, but the structure of the graph changes.  We’d have to carefully consider the pool from which an agent randomly chooses a new friend. If the pool includes all agents in the graph, I’d expect the graph to collapse in on itself (constantly shrinking graph diameter) over time.  If the pool includes just friends of friends, the graph would still shrink, but more slowly.  Is there a way to mutate so that various properties of the graph (like graph diameter) are maintained?

I think social graph mutations are interesting.  Do you agree?