1 Woodrow Wilson, Hide and Seek Politics, 191 N. Am. Rev. 593 (1910).Google Scholar

2 C. O. Mathews, The Effect of the Order of Printed Response Words on an Interest Questionnaire, 20 J. Educ. Psych. 128 (1929).CrossRefGoogle Scholar

3 Henry M. Bain, Jr., & Donald S. Hecock, Ballot Position and Voter's Choice, Wayne State University Studies, Political Science no. 1 (Detroit: Wayne State University Press, 1957).Google Scholar

4 G. J. G. Upton & D. Brook, The Importance of Positional Voting Bias in British Elections, 22 Political Stud. 178 (1974).Google Scholar

5 Christopher Robson & Brendan Walsh, The Importance of Positional Voting Bias in the Irish General Elections of 1973, 22 Political Stud. 191 (1974).CrossRefGoogle Scholar

6 John E. Mueller, Choosing Among 133 Candidates, 34 Pub. Opinion Q. 395 (1970).Google Scholar

7 Delbert A. Taebel, The Effect of Ballot Position on Electoral Studies, 19 Am. J. Political Sci. 519 (1975).Google Scholar

8 Supra note 3, at 10, quoted from Paul Beckett & Walter L. McNutt, The Direct Primary in New Mexico 23-34, University of New Mexico, Department of Government, Division of Research Publication no. 7 (Albuquerque: University of New Mexico, 1947).Google Scholar

9 Evidence to this effect is provided in Robson & Walsh, supra note 5.Google Scholar

10 Sangmeister v. Woodard, 565 F.2d 460 (7th Cir. 1977), cert. denied, 98 S.C. 1516 (1978).Google Scholar

11 Id. at 463 n.3 and 466 n.11.Google Scholar

12 Supra note 3, at 16-17.Google Scholar

13 Sangmeister v. Woodard, 565 F.2d 460 (7th Cir. 1977), cert. denied, 98 S.C. 1516 (1978).Google Scholar

14 Although the rotation eliminates most of the possible interferences, it does not eliminate them all: the relative position of the candidate with respect to his or her two neighbors on each side remains the same except when the candidate is first or last on the ballot.Google Scholar

15 Supra note 3.Google Scholar

16 Id. at 11; the authors tell of a Chicago ward committeeman who, in the days when the position on the ballot was determined by the order of filing, used to wait until the last possible moment to file to secure for himself the last position on the ballot.Google Scholar

17 Supra note 6.Google Scholar

18 With the exception of Edmund G. Brown, Jr. (now governor of California), who had the advantage of high name recognition (his father having served several terms as governor) and who was elected by a large margin.Google Scholar

19 The Illinois State Board of Elections, 1975-2, Regulation, filed Dec. 3, 1975.Google Scholar

20 Very often when probabilities of events are calculated the figures come as a surprise. Quite often, they tend to be inconsistent with the “intuition” of even the most experienced mathematician. The main advantage the latter has is in knowing that his or her intuition is fairly likely to be wrong. Nor are simple probabilistic questions necessarily more amenable to intuitive solutions than complex ones. An illustration of the element of surprise in calculating probabilities is provided by the following classical example: the odds of finding at least two persons with the same birthday in a group of 23 people are better than even (the probability of this event isGoogle Scholar

and in a group of 50 people the odds are better than 32 to 1 (1)Google Scholar

21 For a rigorous mathematical proof of this fact see appendix, sec. 2, formula (2).Google Scholar

22 This is a special case of formula (3) of appendix, sec. 2, for g = 10.Google Scholar

23 This number can also be seen directly from the listing used in the text for case (2): an individual candidate c can occupy the first position in any of the 24 configurations shown and can also appear after a or after b in the first 12 configurations, for a total of 36 favorable configurations in which c occupies any of the first two positions.Google Scholar

24 The total number of possible drawings is (c+ 2)!, which corresponds to the c+ 2 numbers to be drawn. Out of these, following the same analysis presented in the text for the case c= 17, the number of favorable drawings isGoogle Scholar

25 When c= 1, only positions 1 and 3 are possible, while for c= 2 and higher, all positions up to c+ 2 are possible.Google Scholar

26 See note 24 supra. Google Scholar

27 This section deals with the problem as presented. In theory at least the same approach can be extended to facilitate the use of an empirical distribution across different sizes of g. Such an extension would enable the use of cumulative evidence collected over time in a less restrictive way since in practice the size of g varies from lottery to lottery when the number of offices up for reelection varies.Google Scholar

28 The number of candidates in the group petition is also g. There is no problem distinguishing mathematically between the case when this number is equal to the number of persons to be elected and the case when the two are different. This is not done, however, since it would further complicate the discussion by introducing an additional variable (say, p) for the number of persons to be elected, while in practice it is most unlikely that a party would submit a group petition with g≠p. Google Scholar

29 Supra note 3, at 63.Google Scholar

30 Based on formulas (4)-(8) developed in sec. 6 of the appendix.Google Scholar

31 This is formula (4) in sec. 6 of the appendix.Google Scholar

32 This fact can be seen from the following heuristic argument: the probability of occupying one of the first b positions plus the probability of occupying one of the next c + g - b positions is 1 since all possibilities are exhausted. Viewed from the other end, however, the probability of occupying one of the next c + g - b positions is the same as occupying one of the first c + g - b positions. Thus:Google Scholar

andGoogle Scholar

It also follows from here that for b = c + g - b or b = (g + c)/2, the two probabilities equal 1/2, and the value of c for which the preferability switches direction is c = 2b - g. Google Scholar

33 See note 32 supra. Google Scholar

34 This fact follows immediately from the formulas in appendix, sec. 7.Google Scholar