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IRV Used to Rank Voting Systems

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Paul Cohen
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Plurality voting (PV) is an exceptionally simple and widely utilized voting system. Using PV, a voter's only option is to select exactly one candidate to support. This system is used in most U.S. elections, and fortunately, it does perform satisfactorily when there are no more than two candidates. But despite PV being unsuitable for the purpose, many American elections, particularly primaries, depend on it to choose even from many candidates.

Ranked-choice voting (IRV) has been adopted for elections in a few states, so, at least within the U.S., many people are familiar with it. Unfortunately, too many people seem to think IRV is the only available alternative to PV. IRV is an exceptionally complex voting system, but it does encourage voters to vote for their favorite in an election. However, there seems to be little hope that with IRV, the electoral prospects of minor parties will improve much.

Approval voting (AV) is mostly used internally, by academic organizations, so it fails to have much name recognition. But AV does readily accommodate the participation of multiple candidates. An election win by a minor party candidate using AV might be marginally improved in comparison with IRV or PV, but if so, that improvement seems, at best only very slight.

Even less widely known is Balanced Approval voting (BAV); Wikipedia prefers to refer to this system as "Combined Approval Voting", a name that seems unrecognized, even among the few individuals familiar with BAV. BAV is commonly used in Latvia, often for multiple winner elections. BAV not only accommodates multiple candidates, it encourages their participation simply by turning the election of a minor party candidate into a realistic possibility.

Based on familiarity, we should clearly rank these systems in the same order they are listed above. However, such a ranking is not particularly interesting. IRV asks a seemingly better question by asking voters to rank the candidates in decreasing order of that voter's personal preferences. As an exercise, let us see how such preferences might be arranged for an IRV election to select one of these voting systems.

Take Your Pick; Rank them in order of preference.
Take Your Pick; Rank them in order of preference.
(Image by SplodgusMaximus from flickr)
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In several past articles, I have pointed out how unreasonable it is to expect voters to arrange candidates in order as IRV expects. One problem arises, for example, for a voter who considers several candidates to deserve equal support. In elections with many candidates, this is likely to be a common predicament, so the question is important. The only option for the voter is to somehow fabricate a web of lies. The voter must declare preferences between various pairs of them even though those preferences are pure fiction.

And a voter may encounter an unfamiliar candidate on the ballot, so how can the voter rank such candidates? Unfortunately, as common a situation as this may be, IRV fails to permit the voter a satisfactory action. IRV does invite voters to omit candidates from the voter's ballot and a voter may assume that is the proper course to take. However, the effect on the election is appropriate for abstention. The effect is essentially to designate that candidate as being the worst of the worst, ranked even lower than the very last candidate that the voter does list. ï ? ? žï ? ? 

In IRV elections with multiple candidates, it is quite possible, even probable, that no ranking of candidates can honestly reflect a voter's opinions about the candidates. Mostly, the necessary fabrications will proclaim a preference not felt by the voter, but there can also be situations (such as a loop in the voters' actual preferences or perhaps only within the already fabricated preferences) where the voter can find no alternative but to omit mention of what is a true preference of the voter. In one way or another, the data collected from the voters in an IRV election will be distorted. The lies may even outweigh the truth and take control an election.

In an IRV election conducted to choose which voting system to adopt, I could only choose to omit IRV from my list. Appropriately enough (in this instance) this expresses accurately that I consider IRV to be perhaps the worst but at least among the very worst of these four voting systems.

To now consider PV, we first observe that in a PV election with three or more candidates, it is quite possible that a voter would find two of them to be equally qualified for the top rating. So, as with IRV, PV can force voters to make an arbitrary choice and cast a vote that is a lie. But with PV, the much more common corruption of the ballot data is the intrusion of electability as a driving factor for voters in choosing how to vote. In that all too common case, the election winner can easily fail to be the popular favorite among all the candidates; instead, the winner may be the favorite only from among the very few candidates that the voters consider most electable. With PV, electability is a self-enforcing prophesy on the part of people whose judgement on the matter is widely accepted, but no one can know who would be elected by PV if electability were not a consideration.

Is there really a convincing reason to prefer PV over IRV or conversely? With either choice, the election data is apt to be seriously contaminated with many little white lies. But ultimately, all the ballots must be treated as if they were entirely accurate, with every stated preference treated as accurate. In conclusion, neither PV nor IRV vote tallies can be trusted as accurate reflections of voter opinion. I could include neither IRV nor PV in the ordered list on my IRV ballot. This effectively designates both systems as, in my view, simply unacceptable.

The remaining two voting systems, AV and BAV are both evaluative voting systems, and that fact alone makes them more promising. Evaluative voting systems avoid asking voters to compare candidates with one-another. Demanding that level of voter opinion not only would invite error, but it asks for more detail from individual voters than is needed or even particularly useful. An evaluative voting system asks a voter merely to evaluate each candidate in isolation, on that candidate's merit. Only later do these systems evaluate such preferences by interpreting the vote tallies. The vote tallies do measure preferences but, rather than one voter at a time, averaged over all voters. Voting becomes easier, but more important is that the data collected on aggregate voter opinion is considerably less contaminated with errors.

Unfortunately, some inaccuracies are probably unavoidable; voters inevitably make mistakes, for example. And some voters may choose to go rogue, deciding perhaps to pursue some strategic plan. But by not obligating voters to construct a series of lies, evaluative voting systems improve the credibility for election outcomes. Though not entirely eliminated, ballot errors in an evaluative election should be relatively few.

No doubt, some voters will continue to be frustrated by their inability to express, in full and complete detail (perhaps being unable to express an actual preference between two candidates that are marked as equivalent); such problems seem unavoidable. Actual voter opinions can include fine grained nuance well beyond what should reasonably be captured on a ballot; and such details, despite seeming vitally important to a voter, may not be particularly valuable for determining the broad sweep of voter opinion.

There remain two promising voting systems, and in this IRV election, we must still establish what preference is appropriate between AV and BAV. I will explain several reasons why I would rank BAV first, as my favorite of the two.

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Attended college thanks to the generous state support of education in 1960's America. Earned a Ph.D. in mathematics at the University of Illinois followed by post doctoral research positions at the Institute for Advanced Study in Princeton. (more...)
 

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2 people are discussing this page, with 6 comments  Post Comment


Paul Cohen

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You possibly noticed a bit of irony associated with this article. The example of an IRV election to choose a voting system illustrates an exception to all the criticisms it makes of IRV. It may be the exception that proves the rule.

While there are two candidates that I consider equal, they are both unacceptable, and IRV does provide expression for that one very special case. Since I could easily rank the remaining two candidates in order, I had no need to fabricate or ignore any preferences between candidates. For my ballot in particular, the data is accurate. That is no reason to expect any other ballots to be error-free, however.

Submitted on Sunday, Jun 1, 2025 at 6:30:24 PM

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Paul Cohen

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While writing this article, it occurred to me that I chose my words poorly a decade ago in describing the BAV ballot. One of the soft virtues of BAV is that it allows voters to think in terms of compromise. But the word pair for and against fail to convey that thinking and neither do the words support and oppose.

The better words would be the pair acceptable and unacceptable. These words seem to suggest that there can and perhaps should be several candidates in these two groups of candidates, though certainly it is quite possible for a voter to just choose a single candidate in each case.

Submitted on Sunday, Jun 1, 2025 at 6:38:21 PM

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Paul Cohen

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There are several balanced voting systems that have been discussed in some of the earliest articles of this series. One of them, which at one time I called BV-1, but subsequently as Balanced Plurality Voting (BPV), has an group of enthusiastic supporters. BPV is like BAV except it insists the voter choose just a single candidate to evaluate. But notice that BPV is still subject to the two major criticisms made in the article. An arbitrary choice is still necessary when a voter most prefers two candidates equally, but more important it inevitably imposes on the voter a need to consider electability, and even even to give that consideration priority over what the election should surely be measuring, namely voter preferences.

But like BAV, BPV does have an advantage over PV, in encouraging more voter participation.

Submitted on Monday, Jun 2, 2025 at 6:07:12 AM

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"it neither helps nor harms the candidate's prospects of winning election." This is not necessarily true.

Submitted on Monday, Jun 2, 2025 at 9:47:34 AM

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Paul Cohen

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How does adding zero to the net vote help or hurt the candidate's chances of having the largest net tally?

Submitted on Monday, Jun 2, 2025 at 11:58:44 AM

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So how would I vote if one of the other three voting systems were used? Pretty obviously if the election were held using plurality voting I would choose BAV to support. If the election were held with plurality voting I would certainly support BAV, but I would be of two minds about AV; I might feel a need for some vote between abstention and support.

If the election used BAV I would vote opposition to both PV and IRV and I would vote support for BAV. The only difficulty I might have would be in deciding whether to vote support for AV or to abstain; that decision would be a toss-up for me and for any voter who shares my opinions. Some fraction of us would vote support and the remainder would abstain. The effect on the vote totals would be much as if the election provided that fractional vote between abstention and support and all of us took advantage of that intermediate vote.

Submitted on Wednesday, Jun 11, 2025 at 4:32:55 PM

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