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From: radford@calgary.UUCP (Radford Neal)
Newsgroups: net.politics.theory
Subject: Re: Solution to Free Rider problem
Message-ID: <25@calgary.UUCP>
Date: Sun, 5-Jan-86 22:10:21 EST
Article-I.D.: calgary.25
Posted: Sun Jan  5 22:10:21 1986
Date-Received: Mon, 6-Jan-86 04:11:29 EST
References: <20@calgary.UUCP> <2679@umcp-cs.UUCP>
Distribution: net
Organization: University of Calgary, Calgary, Alberta
Lines: 61

> In article <20@calgary.UUCP> radford@calgary.UUCP (Radford Neal) writes:
> >    A promoter for the scheme defines the project and determines how 
> >    much it will cost. He establishes a trust fund to be used to
> >    fund the scheme. Anyone may donate money to the trust fund. No
> >    money is disbursed until the fund contains enough money to 
> >    complete the project. If enough money is not collected by some
> >    specified time, all money is given back to the contributors.
>
> >Would people hold back in the hopes that the dam will be built using
> >other people's contributions, giving them the benefits for no cost?
> >Maybe, but they delay their benefits if they do. The longer the dam
> >goes unbuilt, the less likely it seems that they can get away with this
> >and the more likely they are to contribute what they think is "fair".
> 
> If the resident is interested only or mainly in the benefits to himself,
> he probably won't contribute anything.  The effect of his contribution on
> the probability that the dam will be built is small.  Let's suppose there
> are 10,000 residents concerned, and let's generously assume that his
> contribution of $500 increases the probability, as he judges it, by 1/1000.
> Then the expected monetary benefits of contibuting are $1000 * 1/1000 - $500,
> or -$499.

At last! A sensible argument against my scheme. 

Your mathematics isn't quite right. Remember he gets the money back (with
interest) if the scheme doesn't go ahead. 

The question seems very complex from a game-theoretic point of view. First
of all, there is not a single "contribute / don't contribute" decision. 
He might initially decide not to contribute but change his mind in a 
few months after it turns out other people haven't either. Even if 
we constrain people to make a single irrevocable decision before they know
anything about other contributions, their decision will be affected not
only by how much the contribution increases the probability of the scheme
going ahead (call this dP) but by the probability of it going ahead without
the contribution (call this P). If the benefit is B and the contribution
amount (assumed fixed) is C, the expected return from contributing is
B*dP-(P+dP)*C. Hence, he is more likely to contribute to unlikely projects
in this model. But this is unstable - a likely project would immediately
become unlikely if everyone followed this logic. The analysis is certainly
beyond me.

Various devices might help alleviate the problem:

    1) Make contributions to the fund secret, so no one knows how close
       it is to its goal. After some fixed time period, refund excess
       contributions in proportion to amount contributed.

    2) Make it a part of the trust agreement that all contributions are
       refunded if, say, 90% of the supposed beneficiaries do not 
       make some minimum contribution by the expiry date.

The bottom line which ought to make the scheme work, in the sense that
the dam actually gets built, is that all contributors benefit compared to
the dam not being built. Eventually, people would get tired of not having
a dam and pay up. If they've gone through this before, "eventually" ought
not to be very long.

> --Paul V. Torek, now at umcp-cs!flink, soon at umich!torek

      Radford Neal