This document describes the The University of Chicago Proportional Representation (Hare System). It is a rearranged version of the description distributed by the Secretary of the Faculties in July, 1950 that was modified in July 1985. It was restructured by putting the rules first and the discussion later, since the rules are precise while the discussion leaves many questions open. RULES FOR COUNTING BALLOTS IN PROPORTIONAL REPRESENTATION ELECTIONS 1. The Secretary of the Faculties shall label the ballots so as to achieve a complete random ordering. Appropriate random numbers will also be assigned to each candidate. 2. Sort the ballots, giving each to the candidate marked as first choice. 3. Set aside as invalid any ballots from which the first choice of the voter cannot be clearly ascertained. Count every other ballot valid, whether it is marked according to instructions or not. 4. When all the ballots have been distributed, make a tabulation showing the number of valid ballots credited to each candidate. 5. By adding the numbers of valid ballots of all the candidates, determine the total number of valid ballots cast. 6. Determine the quota that suffices to elect a member by dividing the number of valid ballots by a number greater by one than the number of seats to be filled and adding one to the result, disregarding any fraction that may arise. After each transfer of the ballots of any one candidate, whether the transfer be of the surplus ballots of a candidate who has received quota (see Rules 8 and 9), or of all the ballots of a defeated candidate (see Rule 17), the quota shall be recomputed if the transfer involves any exhausted ballots (see Rule 18). 7. Declare elected every candidate who has received the quota. 8. If this does not fill all the places, transfer if possible, as many of the ballots of each elected candidate as he has above the quota, each ballot to the candidate marked on it as next choice among the candidates still lacking the quota. 9. If more than one candidate has received more than the quota, transfer first the surplus ballots of the candidate with most ballots, then the surplus ballots of the candidate with next most ballots, and so on until the surplus ballots have been transferred. 10. In taking ballots for transfer (either from candidates who have received the quota, or from candidates declared defeated), take them in the order of the random numbers (see Rule 1), the lowest first. 11. As soon as a candidate has received the quota, declare him elected immediately, and transfer to him no ballots in excess of the quota. Before the transfer of an elected candidate's surplus ballots, or of all the ballots of a defeated candidate, note whether the transfer can produce a new winner. 12. As soon as the necessary number of candidates have been elected, declare the election at an end. 13. If any ballot taken for transfer as a surplus ballot of an elected candidate does not clearly indicate the voter's next choice among the candidates still lacking the quota, exchange it if possible for another of the candidate's ballots which does. If none of the candidate's remaining ballots can be transferred, declare the appropriate number of ballots exhausted. (Note the requirement in Rule 6 for recomputation of the quota.) 14. After all the surplus ballots of any candidate have been transferred, make a fresh tabulation of results before making further transfers. 15. After all the surplus ballots have been transferred, declare defeated all candidates with no ballots to their credit. 16. As soon as the number of continuing candidates is reduced to the number still to be elected, bring the election to an end by declaring them all elected. A "continuing" candidate is a candidate as yet neither elected nor defeated. 17. If the election is not thus completed by the defeat of all candidates with no ballots, declare defeated the candidate lowest on the poll and transfer all his ballots, each to the candidate marked on it as next choice among the continuing candidates. 18. In distributing the ballots of a defeated candidate, set aside as "exhausted" every ballot which does not clearly indicate the voter's choice next among the continuing candidates. 19. Whenever all the ballots of a defeated candidate have been transferred without completing the election, make a fresh tabulation of results, declare defeated the candidate then lowest on the poll, and transfer all his ballots, each to the candidate marked on it as next choice among the continuing candidates. 20. Continue this process until the necessary number of candidates have been elected or until only that number remain undefeated. 21. In case of a tie, the ballots of the candidate with the lowest random number will be distributed first. ==== ==== ==== ==== ==== ==== ==== ==== ==== ==== DISCUSSION Purpose. The Hare System is intended to secure the representation of every shade of the electorate's opinion in direct proportion to its numerical strength. What It Seeks to Rectify. Under the usual form of voting for a list of people for a committee or representative body where several are to be chosen, a bare majority of the voters or even a plurality is sufficient to elect. The outstanding example of this system is the method used in this country for presidential electors. Equally glaring is the inequality where but one person is chosen to office in a representative assembly. The following example of a congressional election in Indiana indicates this: Representatives Party Vote Elected Democratic . 291,288 13 Republican.. 166,698 0 Progressives 127,041 0 Others...... 55,807 0 In this instance, while 349,546, or a majority, went without representation, a minority elected all the representatives. This occurs with considerable frequency in American legislative elections. The Mechanics of This Plan. 1. Nominations. Nominations are made by a petition signed by a stated number of voters. Candidates for the Council of the University Senate are placed in nomination by three or more members of the Senate. Any number of nominations may be made regardless of the number to be elected. 2. The Ballot and Method of Voting, A sample ballot is as follows: SAMPLE BALLOT Directions to Voters Put the figure 1 in front of the name of your first choice. If you want to express second, third, and other choices, do so by putting the figure 2 in front of the name of your second choice, the figure 3 in front of the name of your third choice, and so on. You may express as many choices as you please, without regard to the number to be elected. Your ballot will be counted for your first choice if it can help him. If it cannot help him, it will be transferred to the first of your choices whom it can help. You cannot hurt any of your favorites by marking lower choices for others. The more choices you express, the surer you are to have your ballot count for one of them. But do not feel obliged to express choices that you do not really have. A BALLOT IS SPOILED if the figure 1 is put opposite more than one name, or if checks are used instead of numerals to indicate choices. 2 Jones Smith 1 Brown 5 Black 3 Green Grey 4 Wood Stone Clark Etc. The voter in the above case has voted for five candidates in the order of his preference. He has said, in effect, "Brown is my first choice, but if he is not chosen, or if he already has enough votes to elect him, I desire that you count my second choice, Jones, and so on down the list." The Counting of the Ballots: The Quota. The first step in counting the ballots is to ascertain the number of first choices necessary to elect a candidate. This is obtained by the following formula: the number of votes cast + 1 = Quota ------------------------------------------ (divided by) the number to be elected, + 1 For example, in an election in which there were 425 votes cast in balloting to elect 17 members of the Council on one ballot, the quota would be: 425 + 1 = 24. ------------ 17 + 1 Remaining fractions are always discarded. This quota of 24 represents the least number of first choices a candidate may receive and still be declared elected. The extra 1 is added (after the division) inasmuch as, without it, the quota would be 23, and it would then be possible for 18 candidates each to receive 23 votes, whereas only 17 are to be elected. 4. The Counting of Ballots: The Transfer of Votes. The ballots are divided into piles according to the first choices indicated. It will then be found, we may suppose, that 27 have marked Jones as the first choice, that 25 have marked Brown as first choice, etc. In tabular fashion, the results might be as follows, according to the first choices marked: 27 Jones 25 Brown 14 Black 23 Green 16 Wood Jones and Brown, having secured the quota of 24, are declared elected. Jones has 3 more votes than are necessary to elect. As these 3 ballots received by Jones in excess of the quota would be wasted if allowed to remain with him, they are transferred to other candidates. Three ballots chosen by lot are, therefore, removed from Jones' pile and distributed according to the second choice noted on each. If any of these second choices are for Brown, who also has already been elected, the third choice is taken. Of Jones' 3 extra ballots, it is found that, on one, Green is marked for second choice. The ballot is therefore given to Green, who now has 24 votes and is declared elected. On the 2 additional Jones ballots, Black is marked for second choice, raising Black's vote from 14 to 16. Brown's extra votes, those above the number of 24, are then distributed according to second choice, etc. If there are vacancies and if there are no surpluses, all the votes of the candidates securing the lowest numbers are taken from them, there being little chance of their election, and they are distributed according to the second or third or fourth, etc., choices indicated thereon. Election Quotas. 1. The Council. In the coming election 17 regular Councillors will be elected for three- year terms. Consequently, assuming that 425 ballots are cast, the formula for obtaining the quota for the election of 17 members of the Council would be: 425 + 1 = 24. ----------- 17 + 1 2. The Committee of the Council. In the election of the Committee of the Council, to be held after the Council election, assuming that all members of the Council vote, the dividend used in obtaining the quota will be 51. The formula for obtaining the quota for the election of the Committee of the Council of seven members would be: 51 + 1 7. -------- 7 + 1 tfd/june99 -- typo fixed Sept. 2002