Spoiled Again

A recurring criticism of voting methods is the spoiler effect. Proponents of IRV (now often called ranked-choice voting), have long promoted their favorite system based primarily on the claim that it avoids the spoiler effect. Maine fell under the sway of this argument following the election of a governor in an election that was a clear illustration of, not just of the spoiler effect but in fact the most common example of the spoiler effect. In that example there are three candidates with voters widely unable to find much difference between two of them. Most voters would prefer one or the other of these two similar candidates, but with plurality voting, these votes are split between the two and each has fewer votes than for the one distinctive. Using plurality voting, the least popular candidate of the three wins and that surely is not the mark of a satisfactory voting system.

Of course, it remains possible for there to be other examples of the spoiler effect; there might be four or five candidates for example. The critical ingredient seems to be the vote splitting and there might be other reasons for vote splitting (see for example, Condorcet and the Spoiler Effect and Obstruction of Voter Expression).

IRV is not the only voting system that avoids the three-candidate spoiler effect, however. Approval voting (and its balanced counterpart, BAV) avoid the problem by allowing voters to express their approval (and, in the case of BAV, their disapproval) of each of the candidates; in the common example for the spoiler effect, voters can approve equally of the two similar candidates and so have no reason to split their votes between them.

It is interesting though, to consider in detail an IRV election with more than three candidates where all but one being viewed by voters as similar. Consider an election with five candidates. Candidate A is supported by 4800 of the 10,000 voters with the remaining 5200 votes being split between the other four candidates, B, C, D and E, giving each of them roughly 1300 votes (roughly enough to avoid the complication of ties). Clearly with plurality voting, A would win whereas with approval voting or balanced approval voting the winner would be one of the other candidates. But what about with IRV?

Superficially, in the first round of counting IRV votes, one of the similar candidates, B perhaps, would be eliminated and B's 1300 votes would be distributed, nearly equally. among the other similar candidates. For the second round, the three similar candidates would each have roughly 1733 votes and in the third round, the remaining two similar candidates would have roughly 2600 votes. But in the fourth round, the one remaining candidate opposing A would have 5200 votes and so would win the election; the spoiler effect is avoided.

But IRV voting would surely be somewhat different because some voters will have an imperfect understanding of how IRV works. Some voters will not carefully study the vote tally system for IRV; they will just assume the system will properly interpret their intent . Voters are told to list candidates in order of preference; but (since with five candidates there will need to be only four rounds of counting) the ballot provides space for only four of the five candidates. So a voter may puzzle over which one should be omitted?

It would not be uncommon for a voter who thinks A is the worst of the candidates, to think that A should surely appear at the very bottom of their list of preferences as a clear expression of the voters feelings about A. Of course, a voter with a full understanding of how IRV works would omit A from the list of preferences, but it seems likely that some voters would fail to understand how the votes are counted and put A in the last position. Such a voter may list preferences as B, C, D, A instead of B, C, D, E, a choice that would only help A to win. How many would do this is hard to tell, perhaps even the majority. But suppose even just 5% of the voters (260 voters) were to vote in this way? In that last round of counting, A would have an extra 260 votes for a total of 5060 votes making A the winner, though with a narrow margin.

This is an especially troublesome example of the spoiler effect. In this election there are 260 voters who believe that their ballots show clearly that A is their least favorite candidate; it seems very likely that these voters fervently opposed the election of A. What makes the example particularly perverse is not simply that A won the election but that it is precisely those 260 voters who caused A to win the election.

You might wonder about the significance of there being five candidates; what would happen if there were only three, for example? With the same voting the results would not change, but it would be less obvious that there would be so many ballots listing A last. With voters listing two candidates rather than four, they might be more inclined to list their top two favorites and just skip the impulse to list the one they oppose last. An analogy to this is the example in an earlier article of an election with eleven candidates in which every voter's second choice was the same candidate. The second-choice candidate clearly was the best outcome, because none of the candidates had more than ten percent of the vote in the first round; however, with IRV that consensus candidate would be eliminated in the first round. Examples with fewer candidates would behave much the same, but the winning candidate would have a more impressive number of supporters. With eleven candidates, the winner with the support of only 10% of the vote, the failure of IRV is hard to deny.