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progressivism, individualism, and the public ... - Telmarc Group

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The <strong>Telmarc</strong> <strong>Group</strong><br />

PROGRESSIVISM, INDIVIDUALISM, AND THE PUBLIC<br />

INTELLECTUAL<br />

facing an "acquit or convict" choice (in a criminal law case); "convict" is correct if <strong>and</strong><br />

only if <strong>the</strong> defendant has committed <strong>the</strong> crime.<br />

First, <strong>the</strong> CJT.s competence assumption requires (roughly) that each voter's probability<br />

of making a correct judgment exceeds 1/2. While on a particular criminal-law case a<br />

judge may easily be mistaken .say, if <strong>the</strong>re is highly misleading evidence ., surely such<br />

cases are ra<strong>the</strong>r <strong>the</strong> exception than <strong>the</strong> rule, <strong>and</strong> so within <strong>the</strong> large class of related court<br />

cases a voter's rate (frequency) of correct judgments exceeds 1/2.<br />

Hence <strong>the</strong> competence assumption holds. Second, <strong>the</strong> CJT's independence assumption<br />

requires (roughly) that it be probabilstically independent whe<strong>the</strong>r judge 1 is right, judge<br />

2 is right, etc.<br />

While it is true that <strong>the</strong> problem's circumstances .such as evidence observed by all<br />

judges, or <strong>the</strong> process of group deliberation .can make it likely that <strong>the</strong> judges cast <strong>the</strong><br />

same vote (hence are all right or all wrong), probabilistic independence is secured if by<br />

"probability" we mean "probability conditional on <strong>the</strong> problem" : indeed, conditional on<br />

<strong>the</strong> exact body of evidence, process of group deliberation <strong>and</strong> so on, nothing can<br />

anymore create a probabilistic dependence between <strong>the</strong> voters (who do not look on each<br />

o<strong>the</strong>rs' ballot sheets). What has gone wrong in <strong>the</strong> argument?<br />

To justify <strong>the</strong> competence assumption, I have appealed to a variable decision problem:<br />

one that is picked at r<strong>and</strong>om from a class of relevant problems. But to justify <strong>the</strong><br />

independence assumption, I have .xed (i.e. conditionalised on) <strong>the</strong> decision problem: its<br />

particular body of evidence, process of group deliberation, <strong>and</strong> so on. One cannot have it<br />

both ways."<br />

In effect, <strong>the</strong>re are a great many issues which one must assume that are at times in<br />

conflict <strong>and</strong> <strong>the</strong> convergence may very well not occur.<br />

Koriyama <strong>and</strong> Szentzes state:<br />

The classical Condorcet Jury Theorem (CJT) states that large committees can aggregate<br />

decentralized information more efficiently than small ones. Its origin can be traced to <strong>the</strong><br />

dawn of <strong>the</strong> French Revolution when Marie Jean Antoine Nicolas Caritat le Marquis de<br />

Condorcet [1785, translation 1994] investigated decision-making processes in societies<br />

Recently, a growing literature on committee design pointed out that if <strong>the</strong> information<br />

acquisition is costly, <strong>the</strong> CJT fails to hold. The reason is that if <strong>the</strong> size of a committee is<br />

large, a committee member realizes that <strong>the</strong> probability that she can influence <strong>the</strong> final<br />

decision is too small compared to <strong>the</strong> cost of information acquisition. As a result, she<br />

might prefer to save this cost <strong>and</strong> free-ride on <strong>the</strong> information of o<strong>the</strong>rs. Therefore, larger<br />

committees might generate lower social welfare than smaller ones.<br />

These results suggest that in <strong>the</strong> presence of costly information acquisition, optimally<br />

choosing <strong>the</strong> size of a committee is an important <strong>and</strong> delicate issue.<br />

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