New electoral system:

A more democratic electoral system: let’s give Condorcet a go

Benedict Spearritt

Australia has a long history of innovation in all things democratic, particularly with the introduction of Preferential Voting federally in 1918. Originally implemented to avoid splitting the vote between the two main conservative parties, since then it has helped voters of all persuasions to indicate their sincere first choice, without ‘wasting their vote’ and forfeiting their say on the formation of government. Subsequently many Australians think that our use of Preferential Voting sets us apart as one of the most democratic ‘democracies’ in the world. So it may come as a surprise to hear that Preferential Voting is not the most democratic system available for single member electorates, and that it is in fact democratically deficient.

The ‘Condorcet Method’, devised by the French philosopher, mathematician and political scientist, Marquis de Condorcet in 1785, still requires electors to rank candidates in the order that they would like to see them elected. The only difference is in how the votes, and more specifically the preferences of each voter are counted in order to determine the winner.

The Condorcet Criterion states that if a candidate is preferred by a majority of the electorate over all other candidates, then that candidate should win. This sounds reasonable enough, but it doesn’t happen in our current Preferential model. Condorcet simulates many head-to-head battles between all possible combinations of candidates, to find the candidate that is universally preferred by a majority of the electorate. Much like many two candidate first past the post elections would. For instance consider a series of ballots with candidates A, B and C ranked as follows:

Preferences

	1. 2. 3.
45%	A, C, B
35%	B, C, A
20%	C, B, A

The numbers at the top indicate the order in which each group of electors would like to see the three candidates elected. For simplicity the electors have been divided into three groups of 45%, 35% and 20%, although the same principles would apply to more realistic voting patterns. A helpful feature of Condorcet voting is that only one count needs to done to determine the winner, rather than several rounds. As a result all of the information from the ballots can be tallied in one matrix. This advantage would certainly reduce election night hangovers!

	A	B	C
Candidate A	N/A	B [55%] A [45%]	C [55%] A [45%]
Candidate B	A [45%] B [55%]	N/A	C [65%] B [35%]
Candidate C	A [45%] C [55%]	B [35%] C [65%]	N/A
Pairwise results: won,lost	0, 2	1,0	2,0

It can be seen in a simple majority system such as first past the post, that candidate A would be the winner, even though a majority of the electorate clearly favours both other candidates over A. However a Preferential system would be little better. C has the lowest primary vote and is eliminated The preferences of C voters flow to B, making B the winner even though a majority prefers candidate C over candidate B, as would be demonstrated in a two candidate race. To determine the Condorcet candidate we look at the pairwise matchings. A is least preferred to both other candidates by a majority of 55% to 45%, so A is elmininated. There is now only one contest left and candidate C defeats B 65% to 35%, making C the Condorcet winner. Note that in any two candidate race, C would have clearly won against both A and B, so why is it that we tolerate any electoral system which cannot replicate this result?

Unless a candidate initially receives a high enough primary vote, chances are that they will be eliminated from the competition before the final ‘two candidate preferred’ decision, even if more voters prefer them to the winner. Consider the recent case of the electorate of Wentworth, regarded as a possible four-way tussle by some, but realistically only ever a competition between Peter King and Malcolm Turnbull. The final contest was between Labor on 44.52 % and the Liberals 55.48%, but did a majority of the electorate actually prefer Peter King to Malcolm Turnbull? They would have if all of the Labor and Green voters preferred King to Turnbull; the approximate results would have been 56.5% for King and 43.5% for Turnbull. Of course without access to all of the ballot papers, whether King was preferred to Turnbull is pure speculation and even if he were, that wouldn’t by itself guarantee a Condorcet victory.

However it should now be clear that our Preferential Voting system is democratically far from perfect and leaves too much to the chance element of the exact ordering of candidate eliminations and preference redistributions. The outcome of the system becomes especially unpredictable when there are more than two strong candidates as demonstrated in the Wentworth example. The end effect of the PV system is that only the preferences between the two parties with the largest number of votes after preference distribution are considered, and 98% of the time it becomes a quasi first past the post election between the two major parties, albeit without ‘wasted votes’. Hence the term and methodology behind the phrase ‘two party preferred’, a term which has legitimised or at least given credibility to the continuation of the major party duopoly.

A variation of the strategic voting that occurs in first past the post stills occurs under Preferential Voting. Troy Rollo’s article http://www.onlineopinion.com.au/view.asp?article=2413, provides an exellent example of how strategic voting can still occur under our current system. Basically his argument was that Green and Labor voters living in safe Liberal electorates at the last federal election had a much better chance of electing an independent candidate than a Green or Labor candidate, but only if they passed up their true first preferences in favour of an independent, thereby protecting the independent from a premature elimination from the count, which would otherwise see the Coalition candidate win comfortably without a more competitive challenge from an independent.

While a Condorcet method will always pick the Condorcet candidate if there is one, (the candidate a majority prefers over all others) and all other systems will not, there may sometimes be no single Condorcet winner because of an ambiguity in the preferences of the electorate. For instance it is possible for a majority to prefer candidate A over B, B over C and C over A, leading to a ‘circular tie’. Some people regard the possibility of this situation occurring as a deficiency of Condorcet voting, but in the words of Russ Paielli who runs the election methods website http://www.electionmethods.org/ it is not a disadvantage of the system. “Sometimes no candidate beats each of the other candidates. The result is then ambiguous, and the ambiguity must be resolved. Such cyclic ambiguities are true ambiguities in the preferences of the electorate, and the fact that Condorcet accurately reflects them is not a problem with the Condorcet method itself, as is often erroneously assumed.”

One method of resolving an ambiguity is to consider the ‘Schwartz set’, which is the innermost set of candidates for which none inside the set is beaten by any candidate outside of the set. It is then a matter of eliminating the weakest defeat (the smallest majority by which a defeat occurs) and recalculating the Schwartz set until a single winner remains. In our previous example C was the only member of the Schwartz set and no ambiguity resolution needed to occur. This Condorcet method of ambiguity resolution is known as ‘Cloneproof Schwartz Sequential Dropping’ http://en.wikipedia.org/wiki/Cloneproof_Schwartz_Sequential_Dropping. There are many other methods of ambiguity resolution, but CSSD is generally regarded as the best.

In CSSD as in preferential voting, you could have either compulsory or optional preferencing. If optional were to be used it would be best to allow voters the option of giving candidates equal ranking, so that a valid series of preferences could look like 1,2,2,3,4,5,5,5. Voters who haven’t specified a candidate rank could either be considered to have no preference about them or, alternatively, they could be counted as their least preferred candidate. I favour the default ‘no opinion’, because voters already have the option of ranking candidates last. A no opinion for a candidate will mean that the voter is allowing the rest of the electorate to decide their ranking, so no votes are cast for or against that candidate. Antony Green http://www.onlineopinion.com.au/view.asp?article=3338 highlights the possible use of optional preferential voting in order to offset the recent rise in informal voting, something that is relevant whether we have a Condorcet or a Preferential Voting model.

Again, regardless of whether we have a PV or a CSSD system or optional vs compulsory preference allocation, I suggest changes to the requirements for candidates standing for the House of Representatives. These are designed to decrease the number of candidates standing, increase voter knowledge about each candidate and restrict the field to candidates who actually want to win and try hard to do so, regardless of their perceived chances. These changes could be facilitated by increasing the deposit to $1000 (currently at $350) and requiring each candidate to gather at least 100 signatures from voters in their electorate.

In the interests of democratic debate, information and education, I suggest that the AEC do two counts at the next federal election for the House of Representatives. One count would use PV to decide the winner and another count could use CSSD to decide the Condorcet winner. This is arguably the only way that the public could understand and appreciate the Condorcet method and for it to receive widespread support. Currently no ‘democractic’ government uses a Condorcet method, but it is rare for a country to use any sort of preferential model. But a number of organisations have used Condorcet for internal elections, including the Software in the Public Interest corporation and the UserLinux project.

Australia has a long and proud history of electoral innovation, let’s continue the tradition. While we continue to have a parliamentary democracy with single member electorates, we ought to apply the most effective and democratic voting system. Condorcet offers that prospect.