Score Voting, Approval Voting, and Majority Rule

Introduction

Score voting (aka “range voting”), as well as approval voting, are sometimes attacked for not abiding by the majority criterion in all cases. This means that there are circumstances when these methods don't elect a candidate with 51% or more first-place support. Such an outcome with these methods is not catastrophic, and may even be desirable.

A Majority If You Want It

The following is the type of election that critics imagine. A voting bloc with greater than 50% of voters slightly prefers one candidate over the other.  The minority block, on the other hand, exaggerates their ballot to favor the other candidate.

Score Voting (0-9 Scale)

% of voters          Their scores

51%                    C1: 9, C2: 8
49%                    C1: 0, C2: 9

Approval Voting

% of voters          Their approvals
51%                    Approve: C1, C2
49%                    Approve: C2

Score voting (including approval voting) never prevents a majority from getting their way. That majority need only “bullet vote” for their favorite candidate, which interesting enough is exactly what mistaken IRV advocates say they’ll do.

Indeed, there are some cases when bullet voting is a prudent thing to do (more here). The above example is a good illustration of this. If the voters in the majority bloc really wanted to show a preference for one candidate over the other, they can do that. So a result that creates this outcome is an odd one unless the voters are virtually indifferent about who wins. In which case, this is hardly a catastrophe.

But we reiterate, no one is forcing them to do anything. If voters insist on “majority rule”, they are indeed free to vote only for their favorite candidate. But note the distinct difference between that tactic, and the tactic associated with IRV. With Score Voting, no voter will ever have an incentive not to vote for his true favorite candidate. Whereas with IRV, the generally advisable strategy requires “down-ranking” of preferred candidates who seem unlikely to win.

IRV & Majorities

In the 2009 IRV mayoral race in Burlington, Vermont, Democrat Andy Montroll was preferred by a sizable majority (54% to 46%) to the winner, Progressive Bob Kiss. Shortly thereafter, IRV was repealed in Burlington, as well as in other municipalities where it had been in place for a relatively short time.

To get around the IRV “thwarted majority” problem, the Burlington Republicans could have insincerely ranked the Democrat ahead of the Republican. Then they’d have gotten their 2nd choice (Democrat) instead of their 3rd choice (Progressive). This is essentially like voting for Gore in 2000 when you really prefer Nader, so you don’t get Bush. And it has devastating consequences, causing IRV to degenerate into ordinary plurality voting.

Contrived Scenarios

The approval & score bullet-voting example mentioned earlier isn't very realistic given normal expected behavior. But by giving such a far-fetched hypothetical, it gives critics (almost exclusively IRV supporters) a catchy-sounding claim. Conversely, the Burlington election is one that happened in real life.

Note also, that it is also possible to contrive bizarre IRV elections. Consider the following IRV scenario with 1,048,577 voters. The candidates are labeled using letters of the alphabet. The IRV winner is Z, but…

  • Z is ranked first by only 2 voters, which is one ten-thousandth of one percent of the voters
  • Every other voter aside from those two prefers A over Z
  • 524,288 voters, or just under 50%, rank Z in last place
  • A majority of voters prefers every other candidate (except T) over Z
  • S is ranked first by almost 25% of the voters, and ranked second by almost 50% of the voters, and preferred to Z by nearly 75% of the voters

# of voters       their ranking
1                     A>Z
2                     Z
2                     B>A>Z
4                     C>B>A>Z
8                     D>C>B>A>Z
16                   E>D>C>B>A>Z
32                   F>E>D>C>B>A>Z
64                   G>F>E>D>C>B>A>Z
128                 H>G>F>E>D>C>B>A>Z
256                 I>H>G>F>E>D>C>B>A>Z
512                 J>I>H>G>F>E>D>C>B>A>Z
1,024               K>J>I>H>G>F>E>D>C>B>A>Z
2,048               L>K>J>I>H>G>F>E>D>C>B>A>Z
4,096               M>L>K>J>I>H>G>F>E>D>C>B>A>Z
8,192               N>M>L>K>J>I>H>G>F>E>D>C>B>A>Z
16,384              O>N>M>L>K>J>I>H>G>F>E>D>C>B>A>Z
32,768              P>O>N>M>L>K>J>I>H>G>F>E>D>C>B>A>Z
65,536              Q>P>O>N>M>L>K>J>I>H>G>F>E>D>C>B>A>Z
13,1072             R>Q>P>O>N>M>L>K>J>I>H>G>F>E>D>C>B>A>Z
262,144             S>R>Q>P>O>N>M>L>K>J>I>H>G>F>E>D>C>B>A>Z
524,288             T>S>R>Q>P>O>N>M>L>K>J>I>H>G>F>E>D>C>B>A>Z

Majority Not Always the Best?

There are actually scenarios where it may not make sense for a traditional majority to win. More on the majority criterion here.

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