Instant Runoff Voting

Disclaimer: My interest in political science is strictly amateur. Also, my views do not in any way represent those of my employer.

Electoral Reform:

Instant Runoff Voting

and why you should support it

Peter A. Taylor
April, 2000 (last modified 12-25-2009)

I am writing this essay partly in self-defense so that people don't think I'm crazy for circulating a ballot access petition for (a) any minor party, (b) a minor party whose policies I generally disagree with more than most, and (c) a minor party that is prone to acting as a spoiler for the major party that I consider to be the lesser of two evils. The reason I am doing this is because the Green Party is promoting fundamental electoral reform, particularly Instant Runoff Voting (IRV) (#glossary). My interest in electoral reform is largely that I find the two-party system to be an "electoral strait jacket," as evidenced by the very narrow and poorly centered range of debate over such issues as drug policy and health care reform. As Arend Lijphart (1984, p. 114) put it,

If partisan conflict is multidimensional, a two-party system must be regarded as an electoral strait jacket that can hardly be regarded as democratically superior to a multiparty system reflecting all the major issue dimensions.

Richard McKenzie and Gordon Tullock (1981, ch. 10) present a graphical illustration of this point in their discussion of the "median voter model." I have taken some liberties with their chart, but it looks something like Figure 1, where the "top" vs. "bottom" dimension represents some set of issues that doesn't lie neatly on the left-right spectrum. With multiple issue dimensions, it's possible for two parties to look like they're competing for the median voter when they really aren't sure where the median voter is, or when there are institutional or agreed-upon limits to the positions they can take to compete.

Figure 1
Issue Combinations

Neither
x

Libertarians

Uncle Sam In		Uncle Sam
My Wallet, Not	median voter	In My Bedroom,
My Bedroom	x	Not My Wallet

x Greens
x	x
Democrats	Republicans

Both

There are other advantages to IRV as well, such as less sensitivity to campaign spending and more pressure on political parties to nominate centrists. As Polsby and Wildavsky (p. 115) lament regarding the dynamics of modern Presidential primaries,

Where once it was useful to be the second choice of 90% of all delegates, today first choices--even of as few as 30%--are far preferable.

With IRV, second choices are often decisive. In addition to advocating IRV, I will also discuss Proportional Representation (PR), followed by a discussion of the mechanics of IRV and several similar systems.

Instant Runoff Voting

I want to clarify the difference between Instant Runoff Voting (IRV, #glossary) (aka the Australian ballot, aka the Alternative Vote, aka Hare's Method) and Proportional Representation (PR, #discussed below). They are being advocated by a lot of the same people (ie. John Anderson's Center for Voting and Democracy (CVD), and several minor political parties), and some of the ballots look similar, but the arguments pro and con are different.

PR implies diversity in the legislature, with the representatives representing factions that don't necessarily have to cooperate to get their candidates elected. I have seen economists (Buchanan and Tullock, 1962) write about this in terms of "explicit bargaining," and the idea is that legislative deals are made between the various representatives after the election.

IRV produces results more like the Westminster system, aka Single Member Plurality (SMP), aka First Past The Post (FPTP). SMP is the most familiar system in the US, the one used to elect Congress (#example). Here you get "implicit bargaining," where the trade-offs are made in the candidates' platforms, and the voters presumably pick the candidates who make more attractive compromises. If you envision people's views as laid out along a left-right spectrum, the candidates closest to the median voter are supposed to get elected (centrists). The deals are supposed to be made before the election, with the resulting legislature being more or less a rubber stamp for the median voter.

I have two main arguments for IRV. The first is that IRV does a better job than SMP of electing centrist candidates. (I'm a "centrist" in the sense that I want government policies to reflect public opinion as a whole, and not to bounce back and forth between extremes.) In the mid 1980s, Britain used to have large non-centrist Labour and Conservative parties each supported by about 40% of the voters, and a centrist Liberal Alliance supported by about 20%. (The Liberal Alliance are now the Liberal Democrats, and have moved to the left.) The big parties could try to appeal to centrist voters, but it's hard to get voters from another party to switch their support, and it hurts the big parties because of the loss of turnout from their more extremist supporters. The British Parliament, elected by SMP, thus tended to bounce back and forth between the extremes rather than staying in the center. In the US, the comparatively centrist parties are the two large ones, with fringe parties like the Greens and Libertarians (I'm not sure what to say about the Reform Party) that act as "spoilers," tending to self-destructively throw elections away from the median voter in the opposite direction. My second argument for IRV is avoiding oligarchy and the "electoral strait jacket." The worst thing about SMP from my perspective is that it severely undermines any attempt to have more than two viable parties, and so politics under SMP tends to be very oligarchic.

Update (10-31-2010): Daniel Hannan, author of The New Road to Serfdom, argues that US-style primary elections are the main difference between the US and Europe. Bear this in mind when comparing US and other political arrangements. Perhaps I should quit whining and just be grateful for primary elections.

Maurice Duverger said that the tendency for SMP to produce two-party elections is so strong that it comes as close as anything does in the field of sociology to being a natural law. The "mechanical" effect of underrepresenting minor parties in Parliament is reinforced by the "psychological" effect that people don't like giving their support to a party that consistently gets screwed. Another quasi-natural law is that political parties are oligarchal. It is normal for there to be a lot of conflict between party leaders and political candidates, but one thing that makes the US weird is the use of primary elections, which tends to severely undermine party discipline. In Britain, the party leaders usually win these fights. In the US, the candidates usually do.

With Instant Runoff Voting (IRV), there are single-seat districts, as with Single Member Plurality (SMP), but the voters rank their preferences in order (1,2,3,4,5). The ballots are distributed to the candidate ranked first. If no one has a majority, the candidate with the fewest ballots is eliminated, those ballots are redistributed to whomever is next on each ballot, and they are recounted. The process repeats until someone has a majority (#mechanics). If Britain had used this system in the 1980s, the Liberal Alliance would still not have won many elections, given its level of first place support, but its supporters, who were relative centrists, would have determined the outcome between Labour and Conservative. This would have forced the big parties towards the center, to compete for "second preferences" from the centrist party's voters, which tendency is so tragically lacking in politics in Papua New Guinea (PNG) since PNG switched to SMP (see I-IDEA Handbook in #references). There is also no "spoiler" effect with IRV, so it is possible to have several viable parties. This in turn gives minor parties incentives to field reasonable candidates, something that I find sadly lacking in the US.

My point is that if you like the Westminster model, you should like IRV, because IRV implements it better than SMP does. The most serious objection I have heard to IRV is that it is more complicated, requiring voters to be able to count to five (a reasonable ballot size). I tend to dismiss this argument as partisan, but perhaps I am being ungenerous.

Update, 12-25-2009: In Australia, where voting is mandatory and ballots are complicated, there seems to be a problem with "donkey voting," where voters mindlessly write "1,2,3..." and leave as quickly as possible.

Other single-member district election systems

There are other single-seat systems that I also like, and discuss below in the #mechanics and #glossary sections. Condorcet's pairwise comparison method and Nanson's point-based elimination method are like IRV (the 1,2,3... ballots are identical), except that a small centrist party like the old Liberal Alliance would usually win. Instead of eliminating the candidate with the least first-place support, Condorcet goes through the list of candidates two at a time trying to find one candidate who would beat each and every one of the others in one-on-one elections. Sometimes you get a rock-paper-scissors result, and need a tiebreaker. Nanson is more elegant because the tiebreaking process is automatic. The two problems with these are that you need a computer to count the ballots even for a classroom-sized demonstration, which probably makes IRV a significantly easier sell to a skeptical audience, and you may have trouble getting people to sit still long enough to explain these other systems. Approval voting is simpler (SMP ballots, but more than one candidate may be checked) and is a good system if the number of candidates is large.

Proportional Representation

There are several different Proportional Representation (PR, #glossary) systems. There's the Single Transferable Vote (STV) system that Ireland uses, which closely resembles Instant Runoff Voting (IRV), except that there is more than one seat per district. The other main type is Party List, which is what Israel and Italy use. Party List comes in several flavors. Germany uses a "mixed member" system with both SMP and Party List seats. Most Party List systems seem to have multi-seat thresholds (1% for Israel, 5% for Germany) for how much support a party has to have in order to win any seats. There are also some "semi-proportional" systems such as Cumulative Voting. Most democracies have some form of PR. (See Douglas Amy or the CVD website #links below.)

The worst horror story I heard about PR was that in Weimar Germany, extremist parties would agree to sack the Chancellor, then be unable to agree on a replacement. Modern Germany has a rule that you have to agree on a replacement first. Obviously, this is not an issue with a Presidential system. On the other hand, I've heard it argued that some Latin American countries have problems because of the combination of PR with a Presidential system, resulting in #gridlock (see Cox, below). My impression is that SMP systems (ie. Westminster) are more sensitive to the way things work in the proverbial "smoke-filled back rooms," whereas PR systems are more sensitive to the way legislatures work. Amateur reformers like me tend to get upset about smoke-filled back rooms, whereas my impression is that political scientists tend to get more upset about mob rule, military coups, and quirks in the way legislatures work. The "explicit bargaining" of PR is more sensitive to foibles in the ways legislatures work than the "implicit bargaining" of single member districts. While I like PR in principle, whether or not I buy the arguments for it will depend on the details of the particular government it's being proposed for, and what reforms it's bundled with.

Here are some arguments for Proportional Representation (PR):

First, there are some standard arguments you're likely to get from the Center for Voting and Democracy. Perhaps the single most important argument for PR in the US is that #Single Member Plurality (SMP, aka First Past The Post, FPTP, Winner Take All) is unjust because of minority vote dilution, and PR (unlike Instant Runoff Voting) is seen as an alternative to racial gerrymandering. (All single-seat election systems are necessarily "winner take all.") Minorities are highly underrepresented in the legislature under SMP (so are women). This promotes alienation and ill-will between minorities and the overrepresented groups. Low voter turnout in the US is sometimes blamed on SMP because of alienation, lack of clear choices between the major parties, and the low probability of many people's votes contributing to the victory of their candidates ("wasted votes"). SMP typically results in a two-party system that rewards mudslinging and issueless campaigns. The quality of political debate and legislative deliberation suffers from lack of diverse viewpoints (See the Arend Lijphart quote above, and my remarks below about Joycelyn Elders.). SMP rewards gerrymandering, which is impossible under PR (it is almost a contradiction in terms). There are too many "safe" districts where the major political parties do not even have effective competition from each other. US politics often invite the complaint that the major parties aren't different enough to provide a clear choice, whereas British politics often invite complaints about the major parties not being moderate enough. It is possible to make both complaints simultaneously if one regards both parties as being dominated by the same special interests or if one doesn't regard the left-right spectrum as an adequate representation of the issues. Also, money is too important in US politics, due partly to the self-fulfilling prophecy effects of SMP, and it's hard to attack this problem with campaign finance reform without trashing the 1st Amendment. (Front-runner status can be more or less bought in the beginning of a campaign for a party nomination, and SMP punishes voters for supporting any candidate who is not either the front runner or his leading opponent.) Winner Take All also produces a lot of false mandates: a razor-thin advantage that is spread evenly geographically gives "landslide" victories. (This is how I view the "Reagan revolution.")

Another argument for Proportional Representation (PR) is similar to the one I gave above regarding #Instant Runoff Voting (IRV), that PR does a better job than Single Member Plurality (SMP) of ensuring that governments are dominated by centrist parties. Parliamentary systems, where the parties are laid out on a left-right spectrum and no one party has a clear majority, typically put small centrist parties in a position to blackmail the more extreme parties into supporting centrist governments. The Huber and Powell paper I reference below that made this argument presented a statistical case based on public opinion surveys and other surveys that tried to measure where different societies were on a left-right spectrum, and compare this to where their governments were. (This claim may be true in many cases, but unfortunately, there are also counterexamples like Weimar Germany.) So it can be argued that even though PR is an attempt to implement "consensus democracy," it still manages to implement "majoritarian democracy" better than SMP, but probably not as well or as reliably as IRV or Condorcet.

I could also argue that the "explicit bargaining" of a PR legislature is likely to result in better compromises than the "implicit bargaining" of SMP because of information problems. Under PR, I vote for a candidate who thinks like I do, and I count on him to study the issues. I need enough information to judge his loyalty to my political faction, and after that I more or less just trust him. Under SMP, I am voting for someone who is probably not loyal to my faction, and I have to read the fine print on his platform, hope he keeps his word, and hope no major issues come up before the next election that weren't covered by his platform. From this standpoint, the implicit bargaining of SMP lies on a continuum somewhere between the direct democracy of town meetings, where I have to know the details of what's going on, and the explicit, representative democracy of PR, where my representative is really supposed to represent me. My preference for representative rather than direct democracy increases with the size of my town or other political unit. The diversity of a PR legislature probably is also important in so far as the legislature is supposed to be a deliberative body.

Although I argued above that PR can make sense in terms of majoritarian democracy, my preference for PR over SMP is because it makes so much better sense in implementing consensus democracy. I worry about the tyranny of the majority. There is a libertarian slogan, "Democracy is three wolves and a sheep voting on what to have for lunch." In the US, I worry more about special interests forming successions of transient majority coalitions, each one playing and winning a different negative-sum game, with everyone losing in the long run. I particularly don't want a leader of a single party that has less than 50% popular support, but that has narrow majorities in a narrow majority of districts, to be put in a position to be able to make radical changes, especially if the voters' choices were severely limited. Generally, I'm much more concerned with preventing government from playing negative sum games than I am with it being slow to respond. But I am also vexed by the "electoral strait jacket." The "strait jacket" actually bothers me more than my concerns about successions of transient majorities. IRV should be helpful in making government less oligarchic, but PR would do a better job with the "strait jacket" problem and with forcing the wolves to negotiate with the sheep.

Objections to Proportional Representation:

Obviously, there are partisan objections to PR. I suspect that the religious right are overrepresented, and that many of them know it, and want the situation to stay that way. I gather that the "liberal" (social democrat) wing of the Democratic Party is in a similar position with respect to labor and other groups within the party, and all of them are advantaged relative to the groups like the drug policy reform movement that are effectively outside both parties. Joycelyn Elders, President Clinton's former Surgeon General, got sacked for even suggesting that the US study the British "harm reduction" approach to drug policy, despite widespread popular sentiment that the US "War On Drugs" has gone way too far in many respects (ie. persecuting medical marijuana users). I see this sacking as a major victory for the mafia. My perception is that there are significant elements of the Democratic liberal wing who prefer being disproportionately powerful, even though this means that their archrivals in the religious right are also disproportionately powerful.

Another view of politics is that it is dominated by relatively small numbers of wealthy "country club" types or "bourbons" who are prone to using high-profile social issues like race, religion, and drugs as smoke screens, and who are really interested in furthering their own and their friends' fortunes at public expense, unburdened by political ideology. (See Davidson, Race and Class in Texas Politics.) In this view, coherent, competitive political parties are necessary to inform everyone else of what the real issues are and to provide a means of doing something about them. If so, the country club types would surely be opposed to the sort of election reforms I advocate here, but the supposedly "advantaged" ideological factions might actually support the reforms in order to gain a greater measure of independence.

Maurice Duverger's book, Political Parties, brought up the analogy of political factions being like wine in bottles, and the argument that putting wine in a different bottle doesn't change the flavor. Duverger rejected this analogy, and argued that enabling fringe factions to form their own viable political parties changes the way these movements evolve. I argued earlier that different voting systems give minor parties different incentives for what kind of candidates to nominate. Duverger was more concerned with the tendency of partial success at the ballot box in rewarding people for clinging to and propagating irrational beliefs. Weimar Germany comes to mind. Germany now has a 5% threshold a party has to cross in order to be represented in the Bundestag. I'm ambivalent about this.

John Ambler's reaction to my interest in Proportional Representation in the US at the Federal level was to worry about gridlock. The idea is that if the Supreme Court is dominated by members who were appointed decades ago when Party A was popular, the Senate is dominated by members elected 6 years ago when Party B was popular, the President 4 years ago from Party C, and the House 2 years ago by Party D, there are too many places where legislation can be blocked or overturned. It can be argued that "separation of powers" and PR are both means of forcing government to work by consensus, but that both of them together are "too much of a good thing." (See Gary Cox, p. 59 of Reflecting. Cox likes the fact that parliamentary systems call new elections when gridlock gets bad.) Another consensus feature would be to require a supermajority to pass certain kinds of legislation, such as a 2/3 majority in both houses of Congress to pass a Constitutional amendment. This also could be argued to be too much of a good thing if combined with PR.

John Ferejohn (Reflecting, p. 44) raises concerns about "accountability" and "transparency" (being able to tell who to blame when you don't like what the government is doing) in addition to "governability" (avoiding gridlock). Whereas the I-IDEA Handbook points out the advantages of PR in a polarized society (ie. South Africa) in giving the government a sense of legitimacy, Ferejohn is concerned with a sense of legitimacy being hurt by lack of responsiveness of a governing coalition to shifts in popular sentiment.

I have a number of reactions to these objections:

The dynamics of a large group, such as a nation full of independent voters or a legislature with hundreds of relatively independent members, are different from those of a small group, such as a "smoke filled back room" committee composed of the leaders of five cohesive political parties, where the legislature can be counted on to rubber stamp anything the committee decides. Ferejohn discusses this in terms of the "logic of coalition forming" on p. 45 of Reflecting, and Proportional Representation potentially being "too stable," with the same coalition forming despite major changes in public opinion. By the same token, coalitions can be "unstable," shifting frequently despite little or no change in public opinion. The influence wielded by religious zealots in Israel suggests that if conflict is multidimensional, the logic of coalition forming may result in a fringe party's influence being far out of proportion to its numerical strength (see Figure 2).

These differences in group dynamics have several implications. For one thing, the arguments for and against PR may depend on whether US-style primary elections are used or if the political parties are disciplined, British-style. The major US political parties are relatively amorphous.

Another implication is that it matters how the chief executive is chosen. I want executive functions to be uninterrupted and dominated by centrists. Ideally, I would like to see a Constitutional Amendment to abolish the Electoral College, and elect the President by popular vote using #^Nanson's method. I don't like the Westminster system of having the legislature choose the Prime Minister, especially if the political parties are large and cohesive. Israel made a strange compromise, by having the Prime Minister elected by popular vote (SMP, unfortunately), but still requiring him to get the legislature's approval to "form a government." This seems to me to defeat the whole purpose of a popular election for the Prime Minister.

A third implication is that, since US legislative "agenda setters" such as the Speaker of the House and Senate Majority Leader are chosen the same way as the British Prime Minister, I have similar objections to the way these officers are chosen. Currently, these officers are chosen by majority vote in elections that are internal to the respective legislatures. Ideally, I would like to see these officers elected by popular national vote using Nanson's method. (I am also concerned that power within Congress is not uniformly distributed, with the seniority and committee systems. If everyone is more or less a centrist, this may not be such a big deal, but with PR, it may be a bigger problem.) Since PR systems are more sensitive to quirks such as "agenda manipulation" (see Mueller) in the way legislatures work, great care should be taken to minimize these quirks.

A fourth implication is that if you have cohesive political parties, especially using Party List PR, you may need some mechanism to ensure that there is a substantial centrist block or a substantial number of independent centrists. A mixed member system such as Germany's is one way to do this. There is also a method by Robert Loring (Loring Ensemble Rule A, LERa) that does this by combining #STV with #^Condorcet (the Condorcet winner is identified and made exempt from the elimination process). You might consider setting upper bounds as well as lower bounds on the number of seats that can be held by any one party. My prejudices run towards US-style incohesive parties with primary elections, but I am concerned that these do not do as good a job of keeping the voters informed. I also agree with Mosch Virshup that the procedures that the political parties use in choosing candidates are at least as important as the procedures for the general election.

Figure 2 suggests how a pure PR system with cohesive parties could produce a legislature with little influence from centrists, creating problems relating to the "logic of coalition forming."

Figure 2
Difficult Coalition Forming Scenario

Fringe Party 1


x	x
Labor	Conservative

Fringe Party 2

Relative Benefits and Risks

The Single Transferable Vote (STV, #glossary) PR system used in Ireland and the Australian Senate seems to me to be much less risky than Party List PR. STV is like IRV, except that the districts may have as many as 5 seats. Party List more or less means voting for a party rather than a candidate. STV doesn't represent very small political minorities (<20%) very well, but it allows considerable minority representation and offers an escape from the "electoral strait jacket" while still rewarding the parties for being moderate and for courting voters from other parties for their "second preferences." (Ferejohn talks about the "politics of persuation" versus the "politics of mobilization.") Instant Runoff Voting (IRV) would give me maybe 60% of the benefits that I think are possible with an ideal Party List PR system, with essentially no disadvantages as long as the number of candidates on the ballot is kept reasonable (ie. 5 or so). STV would give me maybe 90% of the benefits of Party List, with maybe 20% of the disadvantages. But even in advocating STV, I would want to combine it with IRV, #^Condorcet, or Nanson's method for any single-seat elections, including ones that are internal to the legislature. I note that the US already has a gridlock problem at times, as with the Clinton/Gingrich follies of 1995, so I would advocate one of these single-seat reforms regardless of any movement towards PR.

Then again, democracy only seems to work in some cultures. Maybe majoritarian democracy works in a different subset of these than the ones in which consensus democracy works.

According to a CVD pamphlet, Instant Runoff Voting (IRV) is used to elect the Australian lower house, the President of the Republic of Ireland, the Mayor of London, and the Cambridge, Mass. City Council, and is also used by the American Political Science Association and in assigning the Academy Awards. (It is also used for the Hugo science fiction awards and the Rice University student council President.) I've never heard of anyone actually using Condorcet or Nanson, so that makes IRV safer. It's been tested. This might matter because IRV is biased towards larger parties--candidates with little first-place support get eliminated early. With Condorcet or Nanson, if a lot of voters give second preferences to a minor party candidate that they really don't know much about, in preference over a major party candidate that they know they don't like, their second preferences could easily elect someone they don't know much about and who has not had to pass the scrutiny of a responsible, established party. I see this as an education problem, that the voters need to know not to give second preferences to an unknown, but that doesn't mean that the problem doesn't exist. So Condorcet and Nanson are slightly more attractive to me than IRV, in that they can directly elect centrist candidates from minor parties, but also slightly riskier. I would still advocate Nanson's method for internal votes, such as party primary elections, or other votes where the candidates are relatively well known.

Approval voting is similar to IRV. You vote by checking the candidates you like, but you can check more than one. Whether a Labour Party supporter in the 1980s would also have wanted to check a Liberal Alliance candidate becomes a guessing game (if Alliance does badly, will the Conservative or Labour win?), but it's no worse than SMP, and I expect that in Britain the Alliance would have done well with it, if a bit randomly. Approval voting is good if the number of candidates on the ballot is large, where IRV can get a bit tedious.

The education problem is potentially serious, I think. We had an Irish national co-op student in my branch at work, and I talked with him briefly about their voting system, Single Transferable Vote (STV), which is similar to IRV. He was not old enough to have voted in one of their elections yet, but he told me that his mother had told him that the proper strategy in voting was to put your favorite candidates first, popular candidates that you don't like last, and unpopular candidates in the middle, even if they are worse than the second group. This advice would make sense if they were using the Borda Count (which is one of the reasons I don't like Borda and have not mentioned it until now--see the next section), but not STV. But it's entirely possible that the mythology surrounding the voting system could be more important than the system itself.

Afterthoughts (5-18-2009):

The case study of PNG seems to me to be a compelling argument against FPTP in multi-tribal societies like PNG, but Australia seems to be a different story. When I read about Australian politics, or exchange email with Australians, I am disappointed by how familiar the controversies seem. Australia uses two of my favorite election systems (IRV for the lower house, STV for the Senate), and has considerable representation by minor political parties, but the parties tend to form two semi-permanent coalitions, and the issues seem to be condensed onto pretty much the same left-right political axis as in the US, Canada, and Great Britain.

One possible explanation of this might be that first-world democracies live in a common intellectual pool, and that the ideas that circulate in these countries are determined collectively.

Another explanation is that no matter how many parties there are in the legislature, eventually each bill that is passed has to come up for an up-or-down vote in which all of the parties condense onto one of the two sides. In democracies in which most political factions are cooperative enough to be able to form large working coalitions in the legislatures, these coalitions tend to persist over time, and we thus always end up with a de facto two-party system.

Either way, I am disappointed by how familiar Australian politics seems.

Mechanics of several single-seat voting systems

Consider 1980s British politics, where there was a strong left (Labour) party, and strong right (Conservative), and a weak center (Liberal Alliance). Suppose that Labour has 39% of the vote, Conservative 41%, and Alliance 20% in some electoral district. For sake of keeping the examples simple, suppose that the voters are in three blocks, with their preferences ordered as in Figure 3.

**Figure 3**
**Hypothetical preferences of three blocks of British voters**
	Labour Party 39% of voters	Liberal Alliance 20% of voters	Conservative Party 41% of voters
Labour candidate	1st	2nd (?)	3rd
Liberal candidate	2nd	1st	2nd
Conservative candidate	3rd	3rd (?)	1st

Under Single Member Plurality (SMP), aka First Past The Post (FPTP), the Conservative party wins, and the centrist voters are irrelevant. The winner, the largest cohesive faction, need not be particularly near the center. It is often easier to increase voter turnout among the extremists than it is to woo centrist voters away from other parties. The British government has tended to bounce back and forth between extremes (at least, more so than the US government, where primary elections tend to muddle the internal affairs of the parties and "separation of powers" tends to delay change). Under this system, minor parties act as "spoilers" to the major party they most resemble. The spoiler effect is the standard for perverse outcomes against which the foibles of other voting systems must be compared. Much of the violence associated with SMP elections in Papua New Guinea is related to attempts by various factions to encourage or discourage spoilers. The "insincere" or "strategic" voting whose possibility I lament in other systems is simply taken for granted under SMP.

Figure 4
Single Member Plurality
Candidate	Votes	Result
Labour	39%
Liberal Alliance	20%
Conservative	41%	Winner

Under Instant Runoff Voting (IRV, aka Australian ballot, aka Alternative Vote), the Alliance candidate is eliminated, but the centrist voters who supported it may then determine the outcome of the contest between Labour and Conservative. If the Alliance voters second preferences favor Labour by more than 2% of the total vote, Labour wins. The election tends to go to whichever major party is more successful at wooing the center. Minor parties do no harm to major parties that resemble them and minor parties can hope to gradually grow and become major parties if they appeal to the center. (Apart from being biased in favor of large parties, IRV can sometimes produce "perverse" results where a shift in support from candidate X to Y can cause X to be eliminated instead of Z, which can result in Z winning instead of Y. This is not important in practice because the voters' behavior isn't predictable enough for this to be a basis for "insincere" or "strategic" voting. As "Arrow's Impossibility Theorem" shows, all election systems have some quirks like this; it is nowhere near as perverse as SMP. See Nielsen and de Villiers or Mueller.)

Figure 5
Instant Runoff Voting
Assuming Alliance voters give 2nd preferences to Labour
Candidate	1st Count	2nd Count	Result
Labour	39%	59%	Winner
Liberal Alliance	20%	redistributed
Conservative	41%	41%

Nanson's "Borda elimination" method superficially resembles the "Borda count," which is a point system. Candidates are ranked in order of preference on each ballot, like IRV. Candidates are awarded points according to how highly they are ranked on each ballot. Under Borda count, the most points wins. Under Nanson, the candidate with the fewest points is eliminated, and the ballots are iteratively recounted as if the loser had never existed (lower-ranked candidates on each ballot are promoted). This goes on until there is only one candidate left. If the Alliance party gets second preferences of both the Labour and Conservative voters (which presumably it would, as the center party), the Alliance would score enough points to survive the first iteration, and the candidate who is eliminated first would be determined by the Alliance voters. If the Alliance voters' second preferences are predominantly Labour, the Conservative candidate is eliminated first, and then the Conservative ballots help give the election to the Alliance. Under Nanson's method (or Condorcet or Approval), centrist minor parties can win.

Figure 6
Nanson's Method

First count (3 points for first preference, 2 for second, 1 for third):

Labour	39% * 3 + 20% * 2 + 41% * 1	= 198 points
Alliance	39% * 2 + 20% * 3 + 41% * 2	= 220 points
Conservative	39% * 1 + 20% * 1 + 41% * 3	= 182 points ==> eliminated

Second count (2 points for first preference, 1 for second):

Labour	39% * 2 + 20% * 1 + 41% * 1	= 139 points
Alliance	39% * 1 + 20% * 2 + 41% * 2	= 161 points ==> wins

In this particular example, the Borda count would have produced the same result, but in general, Borda rewards parties for cluttering the ballot with second-rate clones of themselves. This tactic magnifies their initial point totals, but the clones are iteratively eliminated under Nanson's method. Nanson always chooses the Condorcet (pairwise) winner if there is one, and chooses from among the Smith set otherwise (members of the set of candidates that actually participate in any "circular tie"). The mathematical proof of the first point is in the Nielsen and de Villiers book, below, and the second is an obvious extension of it.

Figure 7
Borda Count "Clone" Example

(4 points for first preference, 3 for second, 2 for third, 1 for last)

Labour	39% * 4 + 20% * 3 + 40% * 1 + 1% * 1	= 257 points
Alliance	39% * 3 + 20% * 4 + 40% * 2 + 1% * 2	= 279 points
Conservative	39% * 2 + 20% * 2 + 40% * 4 + 1% * 3	= 281 points
Clone	39% * 1 + 20% * 1 + 40% * 3 + 1% * 4	= 183 points

The Borda count also rewards "insincere" voting--the Labour party could win in the Clone example if between 25 and 36 of their 39 voters ranked the candidates 1-4-2-3 instead of 1-2-3-4, which would contribute points according to 4-2-1-3 instead of 4-3-2-1.

Figure 8
Condorcet ("Pairwise Runoff") Example

Voters rank candidates as with IRV

Alliance beats Labour by	20 + 41	= 61 to 39 %
Alliance beats Conservative by	20 + 39	= 59 to 41 %
Labour beats Conservative by	39 + 20	= 59 to 41 % (moot)

==> Alliance wins, preferred by a majority over each rival.
No circular tiebreaker needed in this case.

It is possible to have a "circular tie," aka "Condorcet paradox," which resembles the child's game, "rock, paper, scissors." Two of three friends wanting to choose a restaurant may prefer Chinese over Italian, a different two may prefer Italian over Mexican, and the remaining permutation of two may prefer Mexican over Chinese. Condorcet requires a tiebreaker in this situation. (It is very hard to contrive a perverse scenario for Condorcet, but the potential need for a tiebreaker creates an opening that makes it possible. By ranking the candidates "insincerely," a faction that is large enough to determine whether a tiebreaker is needed can theoretically decide whether they prefer the Condorcet winner or the tiebreaker winner. Again, this is not important in practice because the other voters' behavior isn't predictable enough for this to be a basis for "strategic" voting. Nanson behaves similarly, but the tiebreaking is implicit, so it's harder to explain how this might happen.)

Approval voting is superficially like SMP, but voters can check more than one candidate. This presents the voters with a guessing game (Is it more important for me to support my second choice against my last choice or to not support my second choice against my first choice?), but otherwise is unobjectionable. It is suitable for long lists of candidates. How the Alliance would have done under approval voting is a recursive guessing game. By my limited knowledge of game theory, Alliance should have done quite well: as long as Alliance approves Labour, Conservatives are forced to approve Alliance, and Alliance wins.

There is Condorcet-Dodgeson, where the tiebreaker is to choose the candidate with the minimax margin of defeat. There is Condorcet-Black, where the tiebreaker uses a point system (the Borda count). I prefer Dodgeson over Black. There are other proposed tiebreakers, too. Nanson's method wouldn't necessarily choose the same winner as either of the above, but it automatically chooses a member of the "Smith set," the set of candidates actually participating in the tie. If there is a tie among A, B, and C, all of whom defeated D, I don't want the tiebreaker to choose D. Again, Nanson is not sensitive to "clones," and the tiebreaking is automatic; the Smith set need not be explicitly calculated. The big advantage I see to Nanson is the lack of need for a tiebreaker.

Glossary

Approval Voting: Like SMP, but you can vote for as many candidates as you like.

Borda Count: Voters rank candidates as with IRV. Candidates get points in proportion to their ranking. The most points wins (one seat per district).

Condorcet: Voters rank candidates as with IRV. Each candidate is compared with each of the others to see who is preferred by a majority. If one candidate wins all of his "pairwise" comparisons, he wins. Otherwise, use a tiebreaker. One winner per district.

Cumulative Voting: PR-lite. There are perhaps three seats per district. Voters get one plurality-style vote for each seat, but may lump their votes together on one candidate if they wish. Results are erratic.

Instant Runoff Voting (IRV): Voters rank the candidates in order of preference (1,2,3...). Ballots go to the most preferred candidate. Whoever gets the fewest ballots is eliminated, and his ballots get redistributed. Repeat until there is one winner.

Loring Ensemble Rule A (LERa): Like STV, but the Condorcet winner is exempted from the elimination process. This assures that the resulting legislature will have a substantial number of centrists.

Nanson: Like the Borda Count, but instead of "the most points wins," the candidate with the fewest is eliminated, and the ballots recounted as if the eliminated candidates had never existed. Repeat until there is one winner.

Party List PR: Voters vote for parties rather than candidates. (This is an oversimplification for some versions of Party List PR.)

Proportional Representation (PR): Multi-seat districts are used. Seats in the legislature are assigned to representatives of various groups of voters in proportion to the size of those groups.

Single Member Plurality (SMP): You know this one. Vote for one candidate only, and whoever gets the most votes wins. No runoffs. One winner per district.

Single Transferable Vote (STV): A PR system with small multi-seat districts, with ballots that look like IRV ballots and are processed similarly. There are multiple winners because it takes fewer than 51% of the votes to claim a seat. Excess votes for winners are redistributed as well as votes for candidates who are eliminated.

Smith Set: The set of candidates who participate in a circular tie using the Condorcet method.

References (in no particular order)

For information about electoral reform in general, visit The Center for Voting and Democracy (CVD).

I strongly recommend George Hallet's critique of the Objections to PR on Douglas Amy's PR Library website.

Reflecting All of Us: The Case for Proportional Representation , Robert Richie and Steven Hill, ed., Beacon Press, Boston, 1999, ISBN 0807044210. This book is notable for the informed skepticism of the chapters by Ferejohn and Cox.

Real Choices/New Voices: The Case for Proportional Representation in the United States, Douglas J. Amy, Columbia University Press, New York, 1993, ISBN 0-231-08154-5. This book is about PR, and says little about single seat reforms such as IRV.

"PR: The Case for a Better Election System," Douglas J. Amy (available from CVD).

Also available through CVD is The International IDEA Handbook of Electoral System Design, published by the Institute for Democracy and Electoral Assistance, with many good case studies, most notably the one on Papua New Guinea. Highly recommended!

Approval Vote web site. Here's another. And here's one with some nice graphics.

Rob Lanphier's site has links to some hard-core technical information and debate, including a Perl script.

Mike Ossipoff's site has more hard-core technical discussion. He also likes Approval Voting.

The people at Election Methods also like Approval Voting. They offer a Python script for Condorcet.

Robert LeGrand's descriptions of ranked-ballot voting methods has detailed examples of how many of these systems differ. This is also hard-core.

Robert Loring's site discusses a number of election systems, most notably his Ensemble Rule A (LERa). Very readable. Has several free software downloads.

Warren D. Smith's Range Voting web site. To me, this looks like it should be very similar to Approval Voting, but I presume that people will vote strategically. Smith claims to have some empirical evidence that most voters don't, at least under this system. I haven't looked at his evidence enough to have much of an opinion one way or the other. Based on an exit poll by Smith, et al, it appears that Range Voting would have produced a significantly different outcome in the 2004 Presidential election than Plurality, even though the minor candidates are still pretty much irrelevant. I find this disturbing, as it suggests to me that Range Voting weighs votes in inverse proportion to the realism and honesty of the respective voters. See the chapter on the Paradox of Voting in Mueller's Public Choice II or Bryan Caplan's discussion of the "rationality of irrationality" in The Myth of the Rational Voter: Why Democracies Choose Bad Policies. I also have a brief discussion of this in Appendix E of my SWUUSI election systems workshop curriculum. No voting system will produce consistently good results in the face of massive voter irrationality, but my impression is that systems that try to weigh the strengths of voters' preferences tend to exacerbate the problem.

Independent Progressive Politics Network

See Is Democracy Fair: The Mathematics of Voting and Apportionment by Leslie Johnson Nielsen and Michael de Villiers, Key Curriculum Press, 1997, ISBN 1559532777 for very readable discussions of Arrow's Impossibility Theorem, Nanson's Method, and voting issues in general. It is an example-oriented high school curriculum book, with examples involving things like camping trips and meat vs. vegetarian pizzas.

"Congruence Between Citizens and Policymakers in Two Visions of Liberal Democracy," John D. Huber and G. Bingham Powell, Jr., World Politics 46 (April 1994), 291-326.

Minority Vote Dilution, Chandler Davidson, ed., Howard University Press, Washington, D.C., 1984. (See Ed Still's chapter for a discussion of STV.)

Race and Class in Texas Politics, Chandler Davidson, Princeton University Press, 1990. ISBN 0691078610

The Electoral College Primer, Neal Peirce and Lawrence D. Longley.

Political Parties, their organization and activity in the modern state, Maurice Duverger, Methuen, London, ISBN 0416683207

Presidential Elections, Nelson Polsby and Aaron Wildavsky, 1988.

Democracies: Patterns of Majoritarian & Consensus Government in 21 Countries, Arend Lijphart, 1984.

See The New World of Economics, 3rd ed., by Richard McKenzie and Gordon Tullock, Irwin, Inc., 1981, ISBN 0256024944 for a discussion of the "median voter model."

See chapter 10 of The Calculus of Consent: Logical Foundations of Constitutional Democracy, by James M. Buchanan and Gordon Tullock, University of Michigan Press, 1962, ISBN 0472061003 for a discussion of "implicit logrolling" (explicit vs. implicit bargaining).

See Public Choice II, by Dennis Mueller, Cambridge University Press, 1989, ISBN 0521379520 for a theoretical discussion of the role of the "agenda setter." This is a very dense, academic economics book, and discusses some sophisticated voting systems suitable for use within legislatures and professional committees. However, Mueller's discussion of the Borda count seems strangely naive after reading Nielsen's and de Villiers' high school curriculum.

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