¹ See, for example, Miller, Warren E. and Stokes, Donald E., “Constituency Influence in Congress,” American Political Science Review, 57 (March 1963), 45–56CrossRefGoogle Scholar; Dexter, Lewis Anthony, “The Representative and His District,” Human Organization, 16 (Spring 1957), 2–13CrossRefGoogle Scholar; Crane, Wilder W. Jr., “Do Representatives Represent?” Journal of Politics, 22 (May 1960), 295–99CrossRefGoogle Scholar; and Erikson, Robert S., “The Electoral Impact of Congressional Roll Call Voting,” American Political Science Review, 65 (December 1971), 1018–32CrossRefGoogle Scholar; Kingdon, John W., Congressman's Voting Decisions (New York: Harper and Row, 1973), esp. Ch. 2Google Scholar; and Clausen, Aage R., How Congressmen Decide: A Policy Focus (New York: St. Martin's, 1973), pp. 126–50Google Scholar.

² Several of these controversies are presented in Fiorina, Morris P., Representatives, Roll Calls, and Constituencies (Lexington, Mass.: D. C. Heath, 1974), Ch. 1Google Scholar.

³ Several political scientists have considered the theory of collective representation. See, for example, Patterson, Samuel C., “Introduction,” in American Legislative Behavior (Princeton: D. Van Nostrand, 1968), p. 4Google Scholar and De Grazia, Alfred, Public and Republic (New York: Knopf, 1951), pp. 5–8Google Scholar. Analyses of the mechanics of electoral representation also, in a sense, are concerned with collective representation. At a more theoretical level, Pitkin, Hanna F., The Concept of Representation (Berkeley: University of California Press, 1967), pp. 216–25Google Scholar.

⁴ Though definitions of “representation” abound, our analysis defines representation as agreement between legislative voting and citizen opinion. The closer the agreement, the “better” the representation. This definition is consistent with notions of representation employed in most empirical analyses of representation. It is identical to the conception of representation guiding the Miller-Stokes analysis.

⁵ Pitkin, p. 61.

⁶ Cited in Pitkin, p. 173. Excellent discussions of virtual representation are also found in Beer, Samuel H., British Politics in the Collectivist Age (New York: Knopf, 1967), pp. 15–20Google Scholar and De Grazia, pp. 36–45.

⁷ Pitkin, p. 175.

⁸ Wahlke, John C., Eulau, Heinz, Buchanan, William, and Ferguson, LeRoy C., The Legislative System (New York: Wiley, 1962), pp. 290–91, 270Google Scholar. Also see Davidson, Roger H., The Role of the Congressman (New York: Pegasus, 1969), pp. 121–26Google Scholar, and Ripley, Randall B., Congress: Process and Policy (New York: Norton, 1975), p. 18Google Scholar.

⁹ We suspect that the non-dyadic nature of organized interest representation in Congress is so “obvious” that it is seldom explicitly mentioned. That is, it is self-evident that a legislator “looking out” for, say, his own peanut farmers will also represent peanut farmers not in his own district. Also see Schwarz, John E. and Shaw, L. Earl, The United States Congress in Comparative Perspective (Hindsdale, Ill.: Dryden Press, 1976)Google Scholar, Ch. 10, for an excellent analysis of how groups such as blacks are represented by non-group members.

¹⁰ We should emphasize that our theoretical concern is the degree of representation, not the predictability of this representation. Merely because some representation can, in a purely statistical sense, be predicted on the basis of a random model does not mean that this representation does not exist. If my member of Congress “votes right” on a key issue it may be irrelevant to me whether this results from random factors or careful attention to my desires.

¹¹ Since our conception of collective representation refers to policy agreement between a majority of all citizens and a majority of legislators, our analysis here further requires the assumption that all legislative districts are of equal population. Unless this were true it would be theoretically possible for a majority of constituencies and a population majority to be in opposition. This assumption is reasonable for the House and unless district size were assumed to be constant, our hypothetical example here would become hopelessly confused. Unequal district size could be included in this analysis, but it would not add anything theoretically important.

¹² The formula of the binomial distribution for the joint probability of independent events is:

Subscripts refer to samples (i.e., 1 = members of Congress, 2 = constituents); the notation is described in Table 1.

¹³ That congressional scores may range 0 to 9 while constituency scores range from 0 to 3 is no problem with a correlation coefficient that “standardizes” these scores. We cannot, however, use standard scores since these would (by definition) yield means of zero in column 2 of Table 3, thus rendering our analysis statistically nonsensical. We should also acknowledge that the mean or any other measure of central tendency can be a poor indicator of what is to be represented, given the wide variety of opinion distribution in a district. It certainly seems politically important whether or not the distribution is bell-shaped or U-shaped. These and several other questions dealing with the measurement of constituency are considered in greater detail in Robert Weissberg, “Some Issues in the Analysis of Legislator Constituency Policy Agreement,” unpublished mimeographed paper.

¹⁴ Our use of legislators' party identifiers as “constituency opinion” (as opposed to, say, the entire district) derives from two considerations. First, of all the groups we could have used, those belonging to a Congress member's party seem the most relevant in terms of representational relationship. Certainly a member of Congress could not be expected to represent everyone in the district or partisans of the opposition party. In any case, the use of the score for the entire district would not change the thrust of our analysis. Second, subsequent analysis considers the theoretically important questions of district minority representation and this requires that we disaggregate district opinions.

¹⁵ Fiorina, Morris P., “Constituency Influence: A Generalized Model and Its Implications for Statistical Studies of Roll-Call Behavior,” Political Methodology, 2 (1975), pp. 249–66Google Scholar; and Kingdon, John W., Congressmen's Voting Decisions (New York: Harper and Row), Ch. 2Google Scholar.

¹⁶ Since concepts like “electoral control” are always troublesome, it might be useful to reiterate that all we mean by “electoral control” is the opportunity available to citizens to determine who shall govern them. The maximum amount of control conceivable would be a political system of one official and one voter. Adding a second voter reduces the first voter's amount of control. Electoral control over one's government would be even further reduced if a second official were added or one were not allowed to participate in the selection process.

¹⁷ Though our main purpose in raising the idea of random selection is to have a baseline model of perfect representation, lotteries for office-holding have a long theoretical and practical tradition. The random-selection principle has appeared in ancient Greece, medieval Spain, and modern jury selection. See Mueller, Dennis C., Tollison, Robert D., and Willett, Thomas D., “Representative Democracy Via Random Selection,” Public Choice, 12 (Spring 1972), 57–68CrossRefGoogle Scholar.

¹⁸ Some interesting data on district safeness and accurate representation ate presented in Miller, Warren E., “Majority Rule and the Representative System of Government,” in Cleavages, Ideologies and the Party Systems, ed. Allardt, Erik and Littunen, Yrjö (Helsinki: Academic Bookstore, 1964), 343–76Google Scholar; also see Fiorina, Morris P., Representatives, Roll Calls, and Constituencies, pp. 90–100Google Scholar.

¹⁹ See, for example, Dexter, “The Representative and His District.” However, also see n. 13.

²⁰ Corroborating evidence on the vulnerability of individual Congress members to national economic events is offered in Kramer, Gerald H., “Short-Term Fluctuations in U.S. Voting Behavior, 1896–1964,” American Political Science Review, 65 (March 1971), 131–43CrossRefGoogle Scholar. Data on how particular members of Congress can be “innocent victims” of economic conditions and presidential popularity are presented in Tufte, Edward, “Determinants of the Outcomes of Midterm Congressional Elections,” American Political Science Review, 69 (September 1975), 812–26CrossRefGoogle Scholar. Actually, the relationship between evaluations of one's own Congress member and the institution of Congress is more complicated than suggested here. Fenno's recent observations on citizens liking their own Congress members while holding a low opinion of Congress as an institution supports our contention that such evaluations can be independent of each other. What is troublesome is why citizens should prefer members of Congress to Congress as a whole when the latter is likely to be more representative than the former. Clearly, as Fenno points out, much more is involved in these evaluations than policy satisfaction. See Fenno, Richard F. Jr., “If, as Ralph Nader Says, Congress Is ‘the Broken Branch,’ How Come We Love Our Congressmen So Much?” in Congress in Change, ed. Ornstein, Norman J. (New York: Praeger, 1975), pp. 277–87Google Scholar.

²¹ Dennis, Jack, “Support for the Party System by the Mass Public,” American Political Science Review, 60 (September 1966), 600–15CrossRefGoogle Scholar.

²² Mayhew, David R., Congress: The Electoral Connection (New Haven: Yale University Press, 1974)Google Scholar.