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Mitchell, E. (2006). Representativity as a scale-independent factor for democratic participation. PHILICA.COM Article number 54.

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Representativity as a scale-independent factor for democratic participation

Ethan Mitchellconfirmed userThis person has donated to Philica (Independent Researcher)

Published in politi.philica.com

Participation rates for direct democracy are known to be inversely related to the scale of the polity. The explained relationship between these two variables, however, is somewhat problematic. Using gender as an measurable example, the author proposes an alternative hypothesis based on representativity. In the case of Vermont town meetings, gender representativity is sufficient to explain 38.9% of variance in participation, without direct recourse to scale.

Article body

Representativity as a scale-independent factor for democratic participation


(With thanks for air support from Abandon Ship, Auto-Ocean, the Bue, and the Frog.)


            Bryan (2004) has demonstrated that participation in Vermont Town Meetings is strongly and negatively correlated to the size of the township.  We infer that for individuals, the choice of whether or not to go to Town Meeting is largely a calculation of size.  Bryan has plausibly suggested that this takes the form of a “voter power” calculus: that voters in a larger polity will feel proportionally less powerful, and thus are less apt to attend.

            The voter power hypothesis is problematic insofar as we cannot extend it to other types of elections.  Voters turn out in large numbers for national elections, in which their single vote cannot possibly make a difference to the outcome.  In Vermont, as the polls close tonight, something like 55% of the eligible voters will have participated, while in the spring, less than half that number will come to the town meetings.

            Slightly less problematic, but still puzzling, is the fact that most of us perform poorly on general-knowledge questions such as the size of our town.  I have spoken to numerous Vermonters who could not guess their town’s population to within plus or minus 50%.  If the heuristics that we use to make attendance choices utilize a logarithm of town population, errors of this sort would seem to introduce considerable noise, even if they ultimately canceled each other out.  

            In an earlier paper (Mitchell 2006), I pointed to a third problem with the voter power theory.  The participation model found by Bryan in respect to majoritarian town meetings is also adequate to describe the participation of Quakers in consensus-based meetings.  In these circumstances, there is no ready equivalent to voter power.

            Based on discussions with other Quakers about their motives, I proposed a different hypothesis.  In this view, people make a decision to participate based on the perceived representativity of their outlook.  If an individual believes that he or she holds common views, and has nothing original to bring to the conversation, they are less apt to attend.  Conversely, if an individual believes that their perspectives will go unheard unless they themselves promote them, they are more apt to attend.

            Quantitative evidence for this hypothesis is difficult to obtain.  First, there is no way to know what people view their own community of interest as being.  As Pew (200) has admirably shown, our constructions of a bipolar political spectrum are completely inadequate to describe the topography of opinion in the United States, and this might be especially true in Vermont, where there are often ten or more political parties on the ballot.  Even if we were to accept, though, that “liberals” and “conservatives” formed distinct and coherent communities of interest, there is practically no way to compare their overall ratios with their attendance at a meeting.

            However, Bryan’s data offers us one rather slender possibility.  We have gendered participation counts for 1433 town meetings, ranging from 1970 to 1998.  Gender represents, to some extent at least, a community of felt interests.  In keeping with the representativity hypothesis, we could argue that people are more motivated to attend if they are concerned that the opposite sex will dominate the meeting.  While gender might not be the strongest political identifier for all participants, it has the merit of being quantifiable to the researcher.  And the line of rationalization that we are proposing is certainly familiar to many Vermonters: “we have to go to town meeting or else everyone there will be old folks / kids / lawyers / farmers / X’s cronies, etc.”  We have to represent.

            Unfortunately, accurate town lists are usually maintained only for a trailing five years, so it is too late to compare Bryan’s figures to primary data on the town’s demographics.  This leaves us with the census figures.  At the town level, the census provides us with gender breakdowns for adults (18+) in 2000; the comparable data for 1990 is, sadly, in a different format.  Comparing the two tables at least reassures us that gender ratios did not change significantly in that period.  Having worked as a census enumerator myself, I have little faith in the accuracy of these numbers, but I doubt there is any systemic bias as far as gender ratios are concerned.  Within the 1990s—I am uneasy about extrapolating any further backwards—there are 442 town meetings in Bryan’s data.

            It is important to recognize that women are proportionately less likely than men to attend Town Meeting in the first place.  The mean Town Meeting (independent of size) is 68% male.  This base rate presumably reflects lingering suppression of female political participation by the patriarchy, and/or a structural challenge wherein the governmental systems created by men are not useful or interesting to meeting the political needs of women, or both.  In any event, it is this basic ratio of 68:32 which we are concerned with.

            Mapping the gender ratio in the polity to with the size of the polity itself produces figure 1:


            First, we note that the gender ratio is heteroskedastic with size: the range of gender ratios narrows as town size increases.  This makes sense, of course: in the absence of some large overriding anomaly, gender ratios should only vary much at low population sizes.  The same should be true for any other quasi-random distribution of traits.  Yet this pattern is much more important than it appears at first glance.  Any quasi-random assortment of the population into n groups will tend to be heteroskedastic, declining with increases in scale.  Thus, the ratio of imbalance between group memberships within a population is a reasonably effective proxy variable for scale.

            This opens up a fascinating possibility.  For even a scale-blind individual can form a relatively accurate impression of ratios.  Put another way, a woman in Baltimore Vermont may not make decisions based on a log-function of her town’s population, but she is apt to be aware that there are more men around her than women. 

            With that in mind, we move to the second chart, comparing gender ratios in the polity with those in the meeting itself:



  This is a fairly classic shotgun scatterplot, with r = -0.14.  But in this case, the lack of patterning speaks volumes.  Apparently the gender makeup of a township is quite irrelevant in determining the gender makeup of a town meeting.  If anything, the minority gender will represent slightly more than usual.  The odds of this pattern occurring by chance are vanishingly low.  The only plausible explanation is that as gender imbalance increases, people in the minority are offsettingly more likely to attend a meeting.

            Combining these observations suggests a rather interesting model.  Let us suppose that each person makes a participation decision based on the local gender ratio.  The probability of their participating is ij/k, where i is the base level of participation (8.2% for men, 3.8% for women).  The ratio j/k describes interest groups (in this case gender), where j is the opposite group, and k is the individual’s own group. This very naïve formula is in fact sufficient to explain 39% of observed variance in our data—and it does so without directly referencing scale. 

            In this model, the individual does not need to have knowledge of the population, nor do they need to make a rational analysis of their voter power in a particular system.  They need only three traits: a sense of political identity or goals; a sense of how widely represented that identity is in the polity; and a heuristic that makes them more likely to actively participate if they feel outnumbered (at least up to a point).  These are very plausible, familiar traits.

            It may be worth examining whether or not such a model has applicability in even larger polities, such as a national election.  In such an environment, to be sure, the j/k ratio would have to be inferred from the media or other outside sources, rather than being a product of one’s own experience.  But we do see numerous campaign strategies that fit this pattern.  Incumbent parties often portray themselves as the underdogs, and stumping politicians often emphasize the uniqueness (i.e. minority status) of whatever audience they happen to be addressing.

            What I would like to suggest, in this very cursory observation, is that a bias towards defending one’s subgroup(s), which is a psychologically compelling motive, will produce the observed negative correlation between polity size and participation, and will do so under a wide range of conditions.


            New Haven, Vermont, night of election 2006.


Works referenced:


Bryan, F. (2004) Real Democracy.  Chicago, IL, USA: University of Chicago Press.

Mitchell, E. (2006). Participation in Unanimous Decision-Making: The New England Monthly Meetings of Friends. PHILICA.COM Article number 14.

Pew Research Center (2005)  Beyond Red vs. Blue.  http://people-press.org/reports/display.php3?ReportID=242, accessed Nov. 7, 2006

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Mitchell, E. (2006). Representativity as a scale-independent factor for democratic participation. PHILICA.COM Article number 54.

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