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The People’s Choice (Round Two)
Lionel E. Deimel

Back in April, I described the pernicious effect of not requiring absolute majorities in elections (see The People’s Choice). Little did I suspect that this effect would play a crucial role in the 2000 Presidential election.

In Florida, whose too-close-to-call election is delaying determination of the next President, Bush and Gore received, X markX markrespectively, 48.84%* and 48.81% of the votes cast. Five third-party candidates—Nader, Browne, Buchanan, Phillips, and Hagelin—each received more votes than separate the two major-party candidates, although only Nader’s 1.63% showing would yield a majority if given to Bush or Gore. Whatever recounts and lawsuits this situation spawns, we can reasonably expect that Florida’s 25 electoral votes eventually will be given to Gore or (more likely) Bush, who will, thereupon, be declared President-elect. This will be true even though more than half the voters of Florida do not want that candidate to be President.

The situation in Florida is surely the nightmare feared by the Gore camp—liberals, who “normally” would be expected to vote for Gore, vote instead for Nader, thereby giving the victory to Bush. Whereas Nader expresses indifference to this “problem” because there is, in his peculiar calculus, no difference between the Republicans and the Democrats, it is likely that most Nader voters strongly prefer Gore to Bush. Many Gore supporters are angry at Nader’s effect on the election, yet it hardly seems fair or democratic to suggest that Nader should not have run or should not have run aggressively. In fact, the problem is in our voting system, not in Nader’s character.

I have been infuriated both by Bush’s insistence that he won Florida and by his supporters’ insistence that Gore is being a bad sport, but I have not gotten around to writing about the situation. Not a problem. Michael Kinsley, editor of on-line magazine Slate just published an essay in Time called “Why Gore Has the Right to Fight.” I highly recommend it.

Whereas most proposals to “reform” the way we elect the President involve doing away with the Electoral College, notice that simply conducting a nationwide popular vote would not preclude electing someone that more than half the voters do not want as President. This problem is independent of the issue of whether election of the President should be by popular vote. In fact, the current impasse actually highlights an advantage of the electoral system. In the case of a close vote, we now only have to deal with demands for local recounts, not for a nationwide recount.

If we want to require a majority vote to determine a winner in an election involving three or more candidates, what alternatives might we consider? The most obvious one, a runoff election among the top two vote-getters, is clearly unacceptable; our election process already seems interminable. The only other reasonable strategy seems to be for the voter to indicate alternative choices along with his first choice for President. By providing alternative preferences, a “most desired” candidate can almost always be found, even if no one receives a majority of first-choice votes. (Ties cannot completely be eliminated, of course.)

Let us call any system that requires the voter to express preferences in addition to his first choice a preference voting system. Any viable preference voting system, I suggest, should have the following properties, which are not independent of one another:

  1. The system should be easy to describe. This follows from the fact that the system must be explained to voters and must be written into law. (No one wants a system only a lawyer can understand.)

  2. The system should not require or encourage complex voting strategy. (The system should not discriminate against the mathematically challenged.)

  3. The effect of voting a particular way should have perspicuous consequences.

  4. The decision required of the voter should not be so burdensome as to discourage voting.

Note that I have not required that any preference voting system be complete, in the sense that it allows the voter to specify his preference in every conceivable circumstance. As a practical matter, however, the advantages of the system must be obvious enough to generate political enthusiasm for its adoption. 

Any system that somehow weights preferences through a “preference function” can, I think, be dismissed out-of-hand. Such a system is simply not transparent enough for general use. Although I had thought that this reasoning precluded the existence of a viable preference voting system, I recently became aware of a system that is actually being used and has all the desired characteristics, though one may quibble about the ease-of-description criteria.

I voted in the recent at-large membership election for ICANN, The Internet Corporation for Assigned Names and Numbers. When I went to cast my ballot, I discovered that I had to rank the seven candidates by assigning “1” to my first choice, “2” to my second choice, etc. It was not clear at the time how this information was to be tabulated. In fact, when the winner was announced and I saw the vote tabulation (click here), I was perplexed. It became clear after a few minutes’ study, however, how a winner was determined. (Mathematically inclined readers may wish to study the ICANN tabulation before reading on.)

The vote tabulation goes through several rounds until a winner is determined. In the first round, all the first-choice votes are counted. If any candidate achieves a majority of the votes cast, that candidate is declared the winner. If no winner emerges, the candidate receiving the least number of votes in the round is declared to have lost. All the votes associated with that candidate are transferred to next-most-desired candidate still in the running. The process continues until some candidate achieves a majority.

A complete concrete example makes this tabulation process clearer. Let us say our election has 5 candidates, A, B, C, D, and E. Twelve voters cast votes as shown below (votes have been ordered and numbered for convenience):


1 1 3 2 5 4
2 1 4 3 2 5
3 1 4 5 2 3
4 1 5 2 3 4
5 2 5 4 1 3
6 3 4 1 2 5
7 3 5 2 1 4
8 4 5 1 3 2
9 4 5 2 3 1
10 5 1 2 4 3
11 5 1 2 3 4
12 5 1 4 3 2

Table 1

Votes are tabulated as shown in Table 2. In Round 1, first-place votes are tabulated. E has fewest votes, so his vote (represented by ballot 9) is given to C, voter 9’s second choice. In Round 2, D is eliminated. Votes from ballots 5 and 7 are given, respectively, to A and C. In Round 3, B is eliminated. Votes from ballots 10, 11, and 12 are all given to C. This results in C’s being declared the winner in Round 4. This result is somewhat surprising, as C was tied for third place in the initial round. (C would not even have been included in a conventional runoff election!) As they say in the polling trade, C does not have the strong positives of, say, A, but neither does he have strong negatives. C is, in other words, a good compromise candidate with broad approval.


Round 1 Round 2 Round 3 Round 4
A 4 4 5 5
B 3 3 3
C 2 3 4 7
D 2 2
E 1

Table 2

This example does not illustrate all the properties of this system of voting. Voters are usually not required to rank all the candidates, so that ballots can be “exhausted” if the voter ranked no candidates left in a given round. Rules need to account for defective ranking and ties of last-place candidates in a given round. Some preferential voting rules immediately eliminate all candidates having less than a fixed percentage of the vote. The example well illustrates the basic features of this voting system, however.

Preference voting systems go by several names, including majority preference voting and instant runoff voting. They are becoming common, if not yet widespread. They are used in many organizations—where a strong two-party system is uncommon—and they are being considered for adoption in a number of states. Both Ireland and Australia make use of such systems in government elections. Preference voting systems are especially attractive to small political parties, such as the Green Party. In a preference voting system, it can rightly be said that the voter can vote his true preference without “wasting” his vote and without aiding candidates he strongly dislikes. (Click here to read an article on this topic in an on-line Green journal.)

Had a preference voting system like the one illustrated above been in use in the past election, Gore would no doubt have received both a significant popularity majority, as well as an electoral-vote majority. Florida would have been in the Gore camp, and we would all be talking about something else.

Readers wanting to know more about preference voting systems should visit the Web site of the Center for Voting and Democracy, which contains a wealth of material on the subject.


*Percentages are computed from information posted by CNN

— LED, 11/11/2000, last revised 2/19/2008


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