No Majority Rule with Plurality Voting
Philip Macklin
I'm delighted to have the opportunity to speak on this topic today. Alan Kyger, mayor of Oxford and a handball buddy from way back, Prue Zimmerman, President of the Oxford League of Women Voters, where I once served as Treasurer, and Bob Ratterman, eminent agent of the Oxford Press, all kindly agreed to be my guests today. My thanks to them and all of you for coming.
This is a political talk in the sense of good government, but not in a partisan sense, so, right up front, let me state my conceptual model. I believe first, the right of decision belongs to the majority and second, the right of representation belongs to all. A corollary to this view is that enabling people to work within the system instead of excluding them from it should be our aim.
While there is much more to good government than just the election system, it is the election system I'm addressing today. I'm not addressing the city manager system or the city manager or the present members of council or council procedures or the merits of city and township merger, or the water tower, or taxation without representation -- just the Oxford Council election system.
Here are the results from the Oxford elections of November 1993. There were 12 candidates for four seats and 2,510 voters, each of whom could cast a vote for up to four candidates. The acronym for this sort of election is ALP--at-large plurality.
Oxford Council Election November 1993
| Pletsch | 1,324 | |
| Cummings | 1,211 | |
| Edwards | 1,079 | |
| Quantz | 854 | 4,468 votes to winners |
| Beerman | 781 | |
| Goodell | 661 | |
| Thacker | 634 | |
| Schroer | 620 | |
| Schnipper | 472 | |
| Brooks | 465 | |
| McCarthy | 313 | |
| Terrell | 233 | |
| Uncast | 1,393 | 10,040 total votes |
"Majority Rule" Loses Its Meaning
As there were 2,410 voters with four votes, there were 10,040 total votes. The winning candidates, the top four, were Pletsch, Cummings, Edwards and Quantz. As a group they received 4,468 votes out of a possible vote of 10,040, or only 44.5%, which is definitely nota majority! Only Pletsch, with 1,324, actually received the votes of more than a majority (1,256) of voters.
Now, without changing the votes cast for the four actual winners, could an entirely different council have been elected? Could even Pletsch, who received votes from more than a majority of the voters, have been defeated in the process? The answer to both of these questions is yes! Let's see how in the following chart:
| Candidate A | 1,393 |
| Candidate B | 1,393 |
| Candidate C | 1,393 |
| Candidate D | 1,393 |
| Pletsch | 1,324 | |
| Cummings | 1,211 | |
| Edwards | 1,079 | |
| Quantz | 854 | 10,040 total votes |
Thus, A, B, C & D, the four above the line, are elected and Pletsch, who received votes from more than a majority of the voters, as well as Cummings, Edwards and Quantz, are defeated and an entirely different set of four is elected!
Just as an exercise, let's see how big a vote a candidate could have, yet not win. The next chart illustrates this hypothetical situation.
| A | 2,009 |
| B | 2,008 |
| C | 2,008 |
| D | 2,008 |
| E | 2,007 | 10,040 total votes |
Thus, candidate E, with votes from 79.96% of the voters, still loses!
Minority Rule Quite Possible
We saw at the beginning that the four actual winners received 44.5% of the possible total of 10,040 votes, definitely less than a majority. Let's see how small the winners' total votes could be, with no uncast votes, and still win. The next chart supplies the answer.
| Winner A | 838 | |
| Winner B | 838 | |
| Winner C | 838 | |
| Winner D | 838 | 3,352 votes to winners |
| Loser E | 836 | |
| Loser F | 836 | |
| Loser G | 836 | |
| Loser H | 836 | |
| Loser I | 836 | |
| Loser J | 836 | |
| Loser K | 836 | |
| Loser L | 836 | 10,040 total votes |
Thus, candidates A, B, C and D -- those above the line -- win with only 33.4% of the votes cast. Further, if the same 838 voters cast all those winners' votes, then only 33.4% of the voters would elect all the winners. Although this is a minimum to win, with no uncast votes, it is not unusual for the large minority to elect all the winners!
Getting Real Majority Rule
To summarize, the present system elected the winners with only 44.5% of the possible total of 10,040 votes, definitely less than a majority. Without changing the actual winners' votes, the system could have elected an entirely different set of four. The system does not assure that a candidate receiving votes from a majority of the voters is elected and could lead to a mere 33.4% of the voters electing 100% of the four winners: i.e., all the winners!
It seems to me that the evidence provides a persuasive case that it is indeed time to change the system!
A system which would assure that the right of decision belongs to the majority and the right of representation belongs to all is proportional representation (PR) using preference voting (or the "single transferable vote"). If, for example, Oxford were electing all seven council members at once with PR, then at least 87.5% of the voters would actually elect all the winners and each winner would have been elected by at least 12.5% of the voters. Further, a majority of the voters, 50% = 4 x 12.5%, would have elected 4 winners, a majority of the seven member council.
The process of voting is simple -- just rank as many candidates as you wish in your preference order and the computer does the rest!
Assuming you want to know in a rough way what the computer is doing, here it is. Initially, it sorts ballots by first choice and declares any candidate with 12.5% or more a winner. If candidates exceed 12.5%, those excesses are distributed by second choice (or third, etc., if the second choice has already won). Then, if fewer than seven have been elected, the lowest candidate is declared defeated and those ballots are redistributed. This process is cycled until seven are elected. No problem for the computer to do all this rapidly and accurately!
Even if Pletsch, Cummings, Edwards, Quantz, Dutton, Kyger and Snavely were the winners, you would know that they (or whatever set was elected) carried the right of decision of the majority of the voters as well as assuring that the right of representation belonged to all.
Philip A. Macklin is professor emeritus of physics from Miami University, Oxford, Ohio and founding member of the Center for Voting and Democracy. He delivered this speech in May 1995 to the Oxford Kiwanis.