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Condorcet Jury Theorem and Voter Capacity
Jesse Richman, 12/7/2021

Review of “The People Cannot Choose a Constitution: Constituent Power’s Inability to Justify Ratification Referrendums” by Jeffrey A. Lenowitz.  Published in the Journal of Politics, Volume 83 Number 2.  https://doi.org/10.1086/709864

In “The People Cannot Choose a Constitution: Constituent Power’s Inability to Justify Ratification Referrendums” Jeffrey A. Lenowitz argues that voter ignorance undermines the normative justification for including a ratification referendum at the conclusion of the process of drafting a new Constitution.  This argument, however, turns on a failure to distinguish between rampant ignorance on the part of individual voters, and the potential for highly accurate informed choices on the part of the voters collectively.  In brief, despite citing Condorcet, Lenowitz doesn’t fully consider the implications of the Condorcet Jury Theorem for the possibility of wise collective choice by voters in the context of the dichotomous choice to ratify or not ratify a Constitution.

Lenowitz is centrally concerned with the constituent power justification for constitutional referenda.  He defines constituent power as “the unique power of the people (or the people themselves when exercising this power) to make and unmake their constitution, the fundamental law that undergirds and creates their state” (p. 618).

Lenowitz asks “What kind of choice must the relevant portion of the population be capable of when they vote on the constitution?”  To which he answers that “voters must at a minimum be able to evaluate the proposed constitution and act upon their evaluation…. Voters must be aware of and understand what they are creating and authorizing… voters need to be able to accurately reference and apply their own values, beliefs, and interests when making their choice. Specifically, in order to satisfy the logic of CPJ, voters must be capable of making what I call a meaningful choice.”

The next paragraph provides a definition of a “meaningful choice” but engages in a critical element of redefinition.  Note that to this point all of the language has been plural.  The referendum choice is after all a collective choice.  Voters as a whole must have been able to do these things.  But in the next paragraph the language is about an individual voter.  “A voter makes a meaningful choice while voting on a ratification referendum: if she understands…” And after that turn the rest of the article points out a variety of evidence concerning the general flakiness of many individual voters, and their extension of that flakiness to their voting on referendums including Constitutional referendums.

This turn to the individual voter is, however, highly problematic in this context.  It ignores the possibility that voters acting collectively could be making a meaningful choice even in the context of widespread and profound ignorance.  It ignores the implications of the Condorcet jury theorem for the potential accuracy of voters’ choices. Jury theorems demonstrate that under a range of conditions, collective choices by highly uninformed voters can lead to an accurate collective choice.  If each voter has only a tiny probability above 50 percent of correctly perceiving the details of the constitution, none the less, the collective choice can exhibit a much greater degree of wisdom.  

Consider the following simple illustration.  Suppose that we must decide between having 55 highly informed citizens (say the constitutional convention itself) simply decide on the constitution, versus having 1 million and one citizens make a decision in a ratifying referrendum. 

Suppose that the 55 citizens have nearly all of the information needed to make a meaningful choice, and that each reaches a correct independent judgment 95 percent of the time.  Suppose that each of the citizens has less information, such that each has an independent probability of making a meaningful choice only 50.5 percent of the time.  That is, they have a 49.5 percent chance of making the wrong choice and a 50.5 percent change of making the right choice.  They are only slightly more likely to get the choice right than they would be if they merely flipped a coin. 

I simulate this using the Binomial distribution.  The probability of interest is the probability of less than a majority making the correct decision. 

  Formula using binomial distribution function
  Probability of failure
55 highly informed voters 0.000000000000000000000374969541829453000
One million and one nearly uninformed voters 0.000000000000000000000007600063865841570
Ratio 49.337683

The probabilities of incorrect decisions in both instances are tiny, but the probability of the million and one uninformed voters making the incorrect decision is substantially tinier – roughly one fiftieth as large.

The nature of a constitutional referendum is well suited to such an analysis: the jury theorems adapt very cleanly to this context.  The alternatives are typically dichotomous “the task of the ratifier is to determine whether she prefers a proposed constitution to the status quo.” P. 621.  With merely two choices, under a range of conditions that are likely but not certain to hold, collective choice will yield the correct outcome – the one that voters would have achieved if fully informed.  For a discussion of such issues see https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118609378.ch10.  As such, a ratifying referendum can be justified as an expression of the consent and a meaningful choice in the exercise of the constituent power of the people.   A large group can make a very meaningful and even rational collective choice that emerges as a result of the aggregation of the admittedly very partial and incomplete information and reasoning capacity available to each one of them.  

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