Subject: Re: is there a statistician in the house? (long)
From: Anthony Long <along@flexiety.com>
Date: Thu, 10 Mar 2005 20:18:29 -0500

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Seth Gordon wrote:

> I have a weird idea for how to address the perpetual question "how can 
> I pay the rent by writing open-source software"?  My idea depends on 
> some statistical techniques that I've read about, but never formally 
> studied.    I'm hoping that someone on this list who knows more about 
> statistics than myself can tell me if I'm onto something useful here, 
> or if I'm just waving my hands.
>
> The community of free-software writers is frequently referred to as a 
> gift economy, where people donate code to the community in order to 
> enhance their own reputation.  I would like to point out two 
> significant things about such economies, in general:
>
> (1) Gift economies are most effective in communities where the donors 
> and recipients are doing the same kind of work.  (Presumably this is 
> because, in the absence of price signals, the shared knowledge of the 
> craft assures donors that recipients will properly appreciate the 
> donors' work.)  In the classic gift economy, the potlatch, everyone 
> involved belonged to a hunter-gatherer tribe.  Pal Erdos's reputation 
> among his fellow-mathematicians was such that many mathematicians let 
> him stay in their homes; professors in other fields would presumably 
> not be so interested in hosting a mathematician, however famous. 
> Open-source hackers have tended to be much more diligent in producing 
> code that their fellow hackers can appreciate than they have been in 
> producing artifacts that benefit other groups (e.g., documentation for 
> non-technical end-users).
>
> (1') Another way of stating this is that there is no global ordering 
> for people's reputations.  If I say that A is a more praiseworthy 
> hacker than B, and you say the opposite, there is no yardstick for 
> judging between us.  Of course, if we both are trying to hire a 
> programmer and we start putting out competitive bids, we will discover 
> whether or not A's labor has a higher *market* value than B's, but 
> then we are no longer in the realm of a reputation-based economy.
>
> (2) Reputation is ordinal, not parametric.  That is, I might say that 
> A is a more praiseworthy hacker than B, but I cannot quantify *how 
> much better* A is.
>
> Now, if there were some way to *transfer reputation* from one person 
> to another, then the effects of (1) could be diluted.  If, for 
> example, my mother told me that a certain piece of free software made 
> her life much much easier and she regarded its author very highly, 
> then even if I personally had no use for that software, I would be 
> favorably disposed towards its author.  How can that transfer of 
> reputation be formalized?
>
> With that introduction, I present The Kindness Of Strangers Game.
>
> (1) The game is played in turns.  (Assume for the time being that each 
> turn lasts one month.)  Players commit to give one another gifts of 
> goods and/or services, and promise that all other factors being equal, 
> they will use the ranking system described below to determine who to 
> give things to.  (A nonrival good given to the entire community, such 
> as an open-source program or an original piece of music, can be 
> accepted as a gift by everyone who appreciates it and ignored by 
> everyone else.)
>
> (2) During each turn, each player announces his or her "donors" and 
> "endorsees".  By naming someone as a donor, you say, "So-and-so gave 
> me some gift in the previous turn, for which I am grateful."  By 
> naming someone as an endorsee, you say, "If you give so-and-so a gift 
> in the next turn, I will be inclined to reciprocate it."  Endorsees 
> can be friends, relatives, gurus, etc.
>
> (3) Your donors are ranked by how much you value their gifts.  This is 
> your "primary rank list".
>
> (4) (This is the statistics part.) The people whom you named as 
> endorsees in the previous turn share their primary rank lists with you 
> in the current turn.  You can combine these lists into a single list 
> as follows:
>
> (4a) Treat each ranking of each donor as an observation; treat the set 
> of rankings received by each donor as a sample.
>
> (4b) Use the Kruskal-Wallis test to find out if there is a 
> statistically significant difference between your samples.  If no 
> donor has significantly better rankings than any other donor, then the 
> only way to combine the lists is to declare a tie between all the donors.
>
> (4c) If the Kruskal-Wallis test *does* find a difference, then use the 
> post-hoc Newman-Keuls statistic to find out who tended to outrank whom.
>
> (Conveniently enough, the Statistics::KruskalWallis Perl module 
> purports to do both these calculations.)
>
> (4d) The list generated by this procedure is your "secondary rank 
> list".   Thus, a person who you never heard of, but who was generous 
> to your friends, may show up highly in your secondary rank list.
>
> (4e) This process may be continued recursively--players may publish 
> their secondary rank lists and use them to compute tertiary lists, 
> etc., etc.
>
> (5) When you are deciding who to favor with gifts in the current turn, 
> you let yourself be guided by the rankings in both your primary and 
> secondary rank lists.
>
> Comments?
>
> How badly am I abusing the statistical techniques I'm referring to here?
>