The Political Vote as a Frequency Distribution of Opinion

Stuart A. Rice
Dartmouth College

Variability is an outstanding characteristic of social data. Whether we are measuring such physical characteristics as height, weight or chest expansion, or whether we are concerned with intellectual capacities or performances, a sufficiently large number of measurements upon homogeneous individuals seems to point invariably to a continuous distribution from the lowest measures to the highest, with a massing of cases at some point on the scale which is usually about mid-way between the two extremes.

It is assumed that if the number of individual cases could become infinite, every position on the scale, however small the gradations, would be represented by frequencies. In practice, frequencies are assembled together during classification around mid-points, so that a distribution which is theoretically continuous is actually presented in any given series as if it were discontinuous or discreet. The measurements given approximate the actual dimensions. This process of classification, it should be noted, is a wholly artificial one in the sense that the number of classes, together with the location of mid-points or class limits, depend entirely upon the will of the classifier, who is presumably guided by the purposes for which the data are to be employed.

There is no reason to suppose that the political opinions held by individuals do not follow the normal frequency distribution which is characteristic of more easily measurable mental characteristics or products. It seems to be true that opinions might be classified in many ways, none of them measurable at present with any degree of exactitude. Nevertheless we are accustomed to distinguish between opinions on either side of a given. issue which are lightly or strongly held, between those which are predominantly emotional and those

( 71) which are predominantly intellectual in character, between those which are moderate and those which are extreme. Thus we recognize variability, and in several directions, but we neglect to note the intermediate positions along these various scales of opinion, because we are unable to do so. Moreover, the democratic concept, in which, according to Bryce,[1] the idea of "one man one vote" is central, has tended to direct attention away from qualitative differences between individual opinions.

It is conceivable that with the development of the technique of mental measurements, qualitative differences in individual opinions might be valued in the process of measuring the collective decision on a given political issue. With respect to the collective decision an prohibition, for example, we might assign greater value to the opinion which was based on scientific analysis of the physiological, social or economic effects of the liquor traffic than to the opinion which represented prejudice, self-interest or casual impression. We might even be willing to weight the opinion which represented strong conviction, relative to the opinion which was weakly held and very near the paint of indifference. According to any one of the possible lines of classification, an average opinion might theoretically be obtained, in which each opinion was weighted according to its place along the scale in the entire distribution.[2]

Modern political society, however, resorts to a crude measurement of opinion by means of the vote. With this device, opinions which would normally be distributed continuously are consolidated into a discreet series, containing but two classes. That is, opinions which would normally fall at all values along the X ordinate are grouped into two classes of pro and con. Instead of smoothing the histogram into a curve, the reverse process occurs : out of the curve is constructed a histogram of two classes containing all of the frequencies in the series.

The class limits, as in the case of every other series, are fixed arbitrarily; but since there are but two classes, each extends in one direction to the extreme value included in its side of the distribution. Hence there is but one class limit to be arbitrarily defined -- the point at which the issue shall be drawn for presentation to the voters. According to the location of this limit on one side or the other of the mode of opinion, the verdict of the electorate will be "for" or "against."

( 72) Statesmen and politicians are successful according to their ability to estimate this modal opinion and define the issues accordingly. It follows that no genuine issue is likely to remain drawn at a point which is far removed from the central massing of opinion. Extremists, sensing the futility of getting their views adopted, or even voted upon, decry political methods and call for "direct action" to secure their ends.

The hypothesis that has been presented may be tested by its application to some leading political issues now before the American people. Among these we may first consider the tariff. It is possible to distinguish five positions in order along a scale which would represent differing views upon this question. These views would be (1) absolute free trade; (2) tariff for revenue only; (3) low protection; (4) high protection; (5) complete isolation, or embargo on imparts. These views may be represented graphically in Figure 1. That each position is relative and shades imperceptibly into the position adjoining, will be apparent if we consider the differences between high protectionists and low protectionists.

Let us assume a legislative body, each member of which is in favor of a tariff, but uninfluenced in his vote by party considerations or factors other than his own opinions. Assume further that this legislature is confronted with the task of fixing the duty upon a specified commodity. Suppose that proposals for an ad-valorem duty are brought before this body, each proposal in turn representing an in-crease of 5 per cent in the tariff contemplated. We should expect with each proposal to find a number of legislators who would desert the high tariff side of the division and go over to the low tariff side. Thus the number of high protectionists and low protectionists, so far as the tariff is judged upon its merits alone, depends entirely on the paint at which the issue is drawn for decision.

In the American Congress the tariff issue has usually been drawn within the ranges of opinion which we have characterized as "low protection" and "high protection." The Republican and Democratic parties, as represented in Congress, have stood for "higher" and "lower" tariffs, respectively. It is obvious that American opinion, as distributed between free trade on one extreme and national economic isolation on the other, tends to mass within a range calling for some kind of tariff protection for American industries. Too great a departure from this central mass of opinion in either direction by the party in power will throw the mode of the distribution of opinion into the class represented by the opposition party, and create a party turnover at the next election.

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In Figures 2 to 5 inclusive the frequency distribution of opinion respecting the tariff which was postulated graphically in Figure 1, has been broken up into a series of bi-segmented histograms to rep-

Figures depicting distribution of Opinions

resent the probable result of a vote, if the issue were drawn. in turn between each two consecutive positions of the five that were distinguished. Thus if the vote were upon the question of free trade (Figure 2) we should expect the persons whose opinions were represented

( 74) by A (in Figure 1) to vote in the affirmative, and those represented by B, C, D and E to unite in the negative. If the vote were upon the question of low protection as. high protection (Figure 4) we should expect A, B, and C to unite in the affirmative against D and E.

The continuous distribution of opinion on another question was indicated by the notable poll an prohibition taken by The Literary Digest.[3] The histogram of opinion, in this case, contained three classes rather than the conventional two presented by an "aye" and "nay" vote. The voter could be recorded either (1) for continuance and strict enforcement of the Eighteenth Amendment and Volstead Law; (2) for modification of the Volstead Law to permit light wines and beers; (3) for repeal of the Prohibition Amendment. The fact that no one of these classes of opinion was represented by a majority of the votes led to claims by the propagandists on both sides that the results represented a victory for their own extreme point of view. "Drys" called attention to the majority against a return to "wet" days. "Wets" called attention to the majority against the existing stringent enforcement laws. Each drew the issue at a different point along the opinion scale.

As still a third distribution of opinion, we may cite the various positions taken upon the question of public ownership. At one extreme the anarchist holds for complete individualism, at the other the extreme socialist would place all industry under state control. In the middle ranges of opinion are to be found those who would nationalize the railways; those who would add coal mines to railway's; those who would add to these the packing plants and the flour mills. It is probable that individual and class interests help to determine the particular industries or services which the individual would be willing to have publicly owned. Hence as to any particular industry, opinion might be multi-modal or skewed. It remains probable that the thorough-goingness of public-ownership opinion in the abstract remains normal in distribution.

If political opinions are distributed in the normal manner that we have suggested, it is probable that radical changes in public opinion occur less frequently than is usually supposed. The relative strength of parties at election time may be changed in either of two ways: In the first, the points at which the issues are drawn may remain constant. Hence, a comparatively slight shift of the modal opinion may bring about a transfer of power from one party to another that appears superficially as a "sweeping verdict at the polls." Nevertheless, the shift is most likely to have taken place within the central

( 75) quartiles of the distribution where opinion most nearly approaches indifference. Subsequent events usually prove in such a case that the changes of opinion were not profound or thoroughgoing. Opinions lightly held are easily changed. Thus the fickleness of public opinion that is so frequently observed may be a phenomenon representing the comparative indifference of the central portions of the distribution of opinion.

In the second case, opinions may remain distributed in the same way, but the points at which the issues are drawn may be shifted. When this occurs, it is usually the result of manouvering for advantage on the part of politicians and party leaders. Old issues are presented in a new light, so that in effect the opinions of the electorate are re-classified and new class limits are established. Any shift of party strength between two elections in which the same issues are presented probably involves both of these occurrences.

There remain to be pointed out the implications of the hypothesis upon movements for political reform. These are more likely to succeed when proceeding step by step, than when presenting their complete program in toto. The mode may be shifted, but slowly. If the political change which is made as a result of the first distribution of opinion proves satisfactory to the voters, the modal shift is likely to continue in the same direction, and successive steps may prove possible.

For example, a distribution of opinion three decades ago with regard to the political rights of women would probably have disclosed the following points along the scale: (1) Women should have no voice in public matters; (2) women should have a voice in voluntaristic organizations, as in church societies, but in no other; (3) women should have the suffrage with respect to school elections; (4) school and municipal suffrage should be given; (5) all suffrage except for national elections should be allowed; (6) complete national suffrage as well as local; (7) women should unite in politics, attempting to secure sex dominance in public matters. With many minor variations, the woman suffrage issue has been drawn in turn between each consecutive pair of these various positions on the scale. The mode of opinion has been shifted constantly in the same direction until it is now to be found, quite clearly, within the group of opinions which sanction all forms of voting equality between men and women. It has not yet shifted to the point at which office-holding for women is regarded with equal favor, nor to the point at which woman's dominance in politics can be regarded as a practical possibility.


  1. Bryce: Modern Democracies, pp. 20-23
  2. An approximation of this idea is contained in the system of plural voting which is based upon property ownership. Where such a system exists, any opinion held by the plural voter is accorded greater value than the corresponding opinion of the citizen with a single vote. The hypothetical system here suggested would grade the opinions, rather than the persons who held them.
  3. Literary Digest, July 8, 1922. Final returns, Sept. 9, 1922.

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