James Green-Armytage
Letter in reply to CVD's "IRV vs. Condorcet" draft analysis
On April 2, 2004, the Center for Voting and Democracy
published a draft analysis about "IRV vs. Condorcet Voting," which
argues the thesis that "IRV is better than Condorcet voting both for
theoretical and pragmatic reasons." The original draft can be found at http://groups.yahoo.com/group/instantrunoff/message/1548
The letter that follows is my reply, which generally argues that they have
placed erroneous criticisms on Condorcet's method, while failing to fully
appreciate its virtues. Text quoted from CVD's draft is in blue
text, and my own reply is in white text.
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Dear Mr. Richie and Mr. Bouricius,
First of all let me say that I do support IRV. I've been living in Berkeley since January, and I supported measure I (to use IRV for city elections).
However, I still think that Condorcet's method of pairwise comparisons is the most profound organizing principle for single winner voting, just as STV is the most profound organizing principle for proportional representation.
I thank you for taking some time to consider Condorcet's method, and to draft a statement addressing your concerns with it. I hope that you intend the statement as part of an ongoing dialogue rather than a final closing-off of dialogue. Of course I don't ask that you devote all of your time to such analysis, but just to keep an open mind on it, and to keep thinking about it when you do have time.
"For example, in some rare cases a voter in an IRV election can hurt a candidate by ranking that candidate more highly. Although technically true, its importance is negligible because such a rare mathematical possibility is almost impossible to anticipate before an election and thus of no tactical significance."
I agree that lacking monotonicity isn't a huge problem for IRV. It does have some tactical significance, but it's not fatal. Actually I think that the problem is theoretically worse in the traditional two round runoff. For example, a case where a Republican had 45% and two Democrats were in a near tie around 22% or 23%. Clever Republicans might vote in the initial election for the Democrat whom they perceive of as being easier for the Republican to defeat. The problem in IRV is analogous to this, but less severe because the Republican's vote would have to stick with the 'weak' Democrat until he got eliminated. Successful exploitation of IRV's lack of monotonicity would indeed be difficult.
"IRV critics who prefer Condorcet also point out that in some scenarios, voters in an IRV system could improve the chances of their second favorite candidate defeating their least favorite candidate by strategically ranking their second choice as number one instead of their true favorite candidate (assuring the strongest acceptable candidate makes it into the final runoff count, for example, ahead of a candidate whom many people like better, but does not have enough centrist appeal to win in a runoff). Because of this example they argue incorrectly that Condorcet voting is the only system that escapes 100% from insincere strategic voting and from the spoiler problem."
I wouldn't argue for a moment that Condorcet (or any other voting method) is 100% free from strategy. I don't think that any other seasoned Condorcet supporters would do so either. Condorcet surely does have strategic vulnerability, and I will get to that soon.
However, the problem with IRV that you are pointing out here is indeed a serious one. This strategy is sometimes known as the "compromising" strategy. In many cases an IRV result will be improved if people in fact do use this strategy. However, communication will become distorted, and the risk of self-fulfilling prophesies appears, such that a voter will worry that their favorite is non-viable, and compromise in favor of another candidate, which will in turn assure that their favorite is in fact non-viable. The fact that voters will be pressured to abandon their true favorite when their preferred lesser-of-two-evils candidate begins to run the risk of early elimination means that IRV retains a strong conservative tendency. That is, it should allow third party candidates to receive symbolic votes and to gain a bit more legitimacy, but it may not make it much easier for them to actually win office, since incentives for the compromise strategy above will kick in precisely at the time when they are about to become really competitive.
This artificial limiting factor to the number of competitive candidates is disturbing because it allows corrupt or otherwise undesirable politicians to stay in place as long as they are preferred over the viable alternative, which is likely to consist of only a single candidate. For example, I will note here that in the Australian House of Representatives (which is elected using IRV), the longstanding Labor-versus-Liberal/National establishment has remained immune to ousters by alternative parties.
Lately I've been trying to look into versions of IRV that allow for equal ranking. Although it wouldn't get rid of this problem altogether by any means, I do believe that it would help somewhat, since instead of ranking their second choice ahead of their first choice, compromising voters could rank them equal to one another. I think that the two methods of equal-rankings-allowed IRV (the version using whole votes and the version using fractional votes) should be looked at carefully.
"In fact Condorcet also creates incentives for insincere voting. All the mathematical elegance of Condorcet Voting is irrelevant when it can be so obviously gamed through insincere strategic voting. Strategic voting occurs when voters have an incentive to rank candidates in an order contrary to their true preferences in order to help a preferred candidate or block another candidate. Although strategic voting may be possible with any voting system, it is in fact a larger problem with Condorcet than with IRV. Suppose four candidates (A, B, C, and D) are running for an office, where candidates A and B are the frontrunners. Consider a voter whose true preferences are in order of A, B, C, D. Under Condorcet, by voting insincerely this voter can minimize the chances that candidate B will defeat his or her preferred candidate A. A voter quickly realizes that the best strategy is to punish the strongest competitor to her favorite candidate by ranking the candidates insincerely A, C, D, B. Doing so may block B - and any candidate -- from becoming the Condorcet winner and improve candidate A's chances to win under the fallback rule. Worse yet, if both A and B supporters widely engage in such strategic voting, the winner could be a candidate most voters actually oppose, but didn't realize would benefit from their insincere rankings. With IRV, there rarely is an incentive to engage in strategic voting, since later rankings do not hurt earlier rankings. In certain unique situations where there is widespread availability of detailed polling information, there are ways to vote strategically with IRV, but strategic voting is greatly limited. There is no rule of general applicability of the value of insincere rankings, as there is with Condorcet."
Your criticism here is generally correct and relevant, although it contains overstatements, such as the sentence: "All the mathematical elegance of Condorcet Voting is irrelevant when it can be so obviously gamed through insincere strategic voting." The strategy you are referring to is sometimes known as the "burying" strategy. I agree that vulnerability to this strategy is a serious problem for Condorcet (in my opinion the only serious problem that the better Condorcet methods have), and it is important to address it just as it is important to address IRV's problems.
I think that any proposal for the use of Condorcet should keep this problem in mind and make sure that there are effective safeguards in place against strategic voting getting out of hand. I myself have been working on developing such safeguard procedures. A few of the procedures I have suggested can be found at
http://fc.antioch.edu/~james_green-armytage/vm/antistratsum.htm
In some cases my proposals involve one or more additional balloting, so they would admittedly be a difficult sell for public elections in the near future. However, in a slightly more advanced society I would advocate them to elect representatives, and in more immediate terms I think that Condorcet procedures can and should be used for other situations where multiple ballotings aren't a problem, such as the process of a legislature deciding between different versions of a bill, or for any voting within a relatively small group. Also, the strategy would be less of a problem in any system where the raw votes were used as the basis for further interpretation rather than producing an instantaneously binding result. This notion will come into play again later.
"Condorcet has even more important negatives directly related to its seemingly sensible goal of selecting the candidate who theoretically would beat all others in a one-on-one race. Its biggest flaw is that it can elect a candidate who has too little support to be seen as a good representative of substantial numbers of voters - a candidate so lacking in support to ever be competitive in a traditional plurality or runoff election."
In passing, I'll to say that I find it somewhat self-contradictory to appeal directly to the methods which you are so deeply critical of to provide a normative argument against Condorcet.
"At an extreme, the Condorcet winner in a four-candidate race might be unable to win a single vote in our current election system, but could win under Condorcet by avoiding being any voters' last choice. In other words, the Condorcet winner's ability to defeat all other candidates in a one-on-one race is entirely theoretical because in an election held under plurality or runoff rules, their lack of core support would prevent then from ever being opposed by just one candidate. Here is an election scenario that demonstrates this problematic dynamic in Condorcet voting. Imagine a polarized election in which: Candidate A is favored by 55% of voters who all disapprove of candidate B, Candidate B is favored by 45% of voters who all disapprove of candidate A. Now suppose candidate C joins the race and stresses his/her likeability and avoids any controversial issues. If 15% of the A supporters are drawn to candidate C's friendly image, the result would now be: Candidate A=40% Candidate B=45% Candidate C=15%. Under plurality rules, Candidate B wins even though 55% of all voters consider Candidate B the worst choice Both IRV and Condorcet always avoid this fatal flaw. Under IRV rules, Candidate C is eliminated in the runoff count and Candidate A again wins with 55%. Under Condorcet rules, however, if Candidate A's supporters rank Candidate C above Candidate B whom they detest, and B supporters also rank C second because of disdain for A, candidate C can win. Because the Condorcet winner may be someone who nobody considers a particularly good candidate, it punishes candidates who take clear stands on controversial issues and rewards candidates who say little of substance. Theoreticians must understand that the measuring tool (the voting system) can change candidate behavior and the information voters have for assessing them. The logic of Condorcet promotes a campaign strategy that is detrimental to political discourse and voters' ability to get the information needed to assess candidates. It primarily encourages avoiding alienating voters, and discourages taking stands on potentially divisive issues. Over a series of Condorcet elections we believe most major candidates would avoid taking clear policy stands, and in turn thus likely lead to lower voter turnout and less well-informed voters."
On this point I have multiple objections. The simplest objection is that I simply don't think that polarized elections, and the polarized two party structures which result, are a good thing. In fact I think that they're terribly destructive. I think that our own political system is a dire example of this. Democrats and Republicans not only disagree with each other, but actually hate each other passionately, across the country. The incentives are for the Democrats to do everything they can to make the Republicans look bad, and vice versa. This is massively counter-productive and leaves little room for compromise. I agree that IRV would maintain more of the polarization of the plurality system than would Condorcet, but I view this as a drawback rather than an advantage.
The next objection is to your assertion that Condorcet would favor candidates who do not take stances on the issues. I don't think that it is a fair assessment. I think that a more plausible statement is that Condorcet favors candidates who stand with the median voter on the issues.
Here I'd like to make a semi-digression which is closely related to this point. I'd like to suggest that Condorcet may be more immediately applicable for voting directly on issues than it is for voting on representatives. I suggest that Condorcet-efficient methods would have the potential to give us effective compromise solutions to social problems, which would be far more valuable and productive than having two polar options battling it out in an all-or-nothing conflict without a middle ground.
For example, let's say that there was a ranked-ballot
public vote in a given state between three options:
1. Legalize gay marriage
2. Allow civil unions between same-sex couples
3. Allow neither civil unions or gay marriage
Let's say that the votes are cast as follows:
35: marriage > civil > neither
6: civil > marriage > neither
19: civil > neither > marriage 40: neither > civil > marriage
Use of IRV would result in the 'neither' option. A plurality vote would also result in the 'neither' option and a single up-down vote on legalizing gay marriages would fail. However, Condorcet reveals the civil unions to be a majority-supported compromise. I think that Condorcet is by far the best bet if you want to find effective compromise solutions, provided of course that a sufficient compromise option exists on the ballot.
Here's a similar imaginary example of an vote on three
options: legalizing marijuana, reducing penalties for marijuana use, and
maintaining the current penalties:
33%: legalize > decrease > maintain
16%: reduce > legalize > maintain
16%: reduce > maintain > legalize
35%: maintain > decrease > legalize
Again, in this example the 'reduce' option is a majority-supported compromise, even though 'maintain' would win with both plurality and IRV.
I think that if we looked at public decision-making as a series of compromises rather than all-out warfare between totally incommensurate belief-systems, we would have a much healthier and more responsive political system. So, whether or not you think that Condorcet should be used to elect representatives, I hope that you will agree with me that it should be used to tally direct votes between more than two options. Please let me know what your thoughts are on this. My current proposal is for a direct democracy system that incorporates proxy voting, is tallied by pairwise comparison, and is legally non-binding while exerting strong political influence. A draft of the proposal can be found at
http://fc.antioch.edu/~james_green-armytage/vm/proxy.htm
So, to come back to my earlier point, I believe that Condorcet would support candidates who take a median stance, and indeed candidates who are able to generate effective compromise positions, rather than candidates who take no stance at all. All other things being equal (which they never are, of course, but the point here is to illustrate a tendency), candidate A will win her pairwise contest with candidate B if A's stance on a given issue is median and B's is not. Surely no candidate could be expected to have a median stance on absolutely every issue, but it is a good direction to move towards.
The 40%-45%-15% example you gave to illustrate Condorcet's flaw is implausible because in it there is no serious centrist candidate. In a real Condorcet election which people actually wanted to win, there would most likely be more than one or two contenders for the centrist position. We wouldn't see two well-expressed wing candidates and a lone, skulking stealth candidate; we would see several candidates seeking the political center. And here I'm not talking about the center as an abstract notion defined by pundits, etc. I'm talking about a democratic definition of the center: the actual position of the median voter in an engaged electorate. This would be a valuable process because it would give the nation an opportunity to explore and seek its own political center. It would give people an opportunity to try to move the center on a given issue by gradual intervals, rather than in chaotic all or nothing bounds. I think that one of the principle weaknesses of our current system is that it does not enable us to know where our political center is, or to act from it, develop it, to keep it flexible and responsive.
I think that an ideal PR system would achieve this, in that it would provide representation for a wide diversity of viewpoints while allowing the center to hold sway on each issue. I think that a good direct democracy system would achieve this as well, as long as the tally system was Condorcet efficient and effective compromise solutions were included on the ballot.
So yes, a bland, inoffensive candidate might do well in Condorcet if his only opponents were two wing candidates who were highly antagonistic to one another, but that isn't a realistic situation. Actually there would be multiple candidates attempting to define themselves into the political center, show themselves to be effective problem solvers, demonstrate that they are free from corruption, and gain the public trust. I think that I as a voter would prefer a candidate who takes a stance on an issue that isn't in line with my own and yet is reasonable and isn't at the opposite extreme, to a candidate whose stance on that issue is unknown to me. Basically I would be suspicious of the latter candidate, and I think that most voters would share this sentiment. If so, then such a candidate wouldn't stand a chance in a Condorcet election.
"IRV provides a better balance between the competing values of being representative of substantial numbers of voters and of having broad appeal. IRV encourages candidates to distinguish themselves and to have sufficient boldness to win many first-choice rankings, but it also encourages candidates to reach out to supporters of other candidates and avoid vilifying them in overly negative attacks. This is a desirable incentive package. A voting system does not just select winners. A voting system shapes the nature of political debate, and largely dictates how well informed most voters are able to be. An inoffensive candidate who studiously avoids taking any controversial stands, but simply campaigns by projecting an image of being friendly and honest can be everybody's acceptable compromise and win with Condorcet even if nobody considered him/her the best candidate. While plurality voting over-values the ability to be a voter's first choice, Condorcet overvalues the value of ability to avoid being voters' last choice. IRV provides a compromise by giving appropriate weight to both values."
I have two objections to the 'strong support versus broad support' argument. The simplest is that it is theoretically possible for a candidate to be a Condorcet winner as well as having the most first choice votes, and yet to lose in IRV. For example:
17%: far right > right > center > left >
far left
18%: right > center > far right > left > far left
16%: center > right > left > far right > far left
16%: center > left > right > far left > far right
17%: left > center > far left > right > far right
16%: far left > left > center > right > far right
So the first choice votes are as below, and subsequent
choices never skip a place on the spectrum.
far left left
center right far right
16
17
32
18 17
In this example the center candidate is the first choice of by far the most voters, wins all of his pairwise comparisons with great ease, and yet 'right' is the winner in IRV.
This is something of a side point though, as your assertion that IRV places more importance on first choice votes than Condorcet is generally correct.
My deeper argument against the 'strong support versus broad support' argument does not rely on such examples at all, but rather questions whether a first choice vote necessarily indicates 'strong support', or a second choice vote necessarily indicates 'weak support'. My belief is that such assertions simply cannot be made, as there is no inherent utility value or emotional value to the different ordinal places on a ballot. Instead, I believe that the position of one candidate on a ballot only derives significance from its relation to the position of other candidates. This is why I believe that the pairwise count method is indispensable. Over the summer I wrote a brief essay which attempts to drive this point home. The writing could use an overhaul, but nevertheless in case you're curious the essay can be found in its current form at
http://fc.antioch.edu/~james_green-armytage/vm/value_of_first_choice.htm
In closing, I'll say that I imagine Condorcet to have been something of a hero, a genius with a good heart who was killed by the Jacobins because he was forthright about his beliefs and cared more about truth and social progress than about making the right move politically. I would like to honor his memory by treating his ideas with the respect they deserve, and I look forward to a time when society will be ready for them.
Sincerely,
James Green-Armytage