Why not Instant-Runoff Voting (IRV)?

Instant-Runoff Voting (IRV) also known as the Alternative Vote (AV) is easy. As for other preferential systems it can be done with the exact same ballots as FPTP, and with the exact same single-member electoral districts; it just needs a change in how we mark the ballots, and how we count them. (And has long and widely been used in Australia state and federal elections as well as in many other places in the world.)

IRV is easy to describe, easy to understand, and easy to count:

  1. On each ballot the voter just marks the candidates in the order of his or her preference, from 1 meaning most preferred, 2 meaning next preferred, and so on;
  2. All the ballots are then counted, considering the first-preference candidates; if this results in a candidate receiving a majority of ballots then that candidate is elected, and we’re done;
  3. Otherwise we eliminate the candidate having at that point the lowest number of ballots, and reallocate the eliminated candidate’s ballots in terms of their indicated next-preference choices, and so on, until a majority candidate is determined or all ballot options are exhausted. (With Ranked Pairs we evaluate all preferences holistically without eliminating candidates.)

In the end we get a winner elected on a better majority basis than FPTP, which is desirable.

Note that there is only one voting step, but the reallocation of the votes for eliminated candidates involves multiple counting steps, and requires consideration of all the results from all the polls in order to do this.

It is important to emphasize that under IRV:

  1. A ballot’s second preference is relevant only if the given ballot’s first-preference candidate is eliminated. If this second-choice candidate is not at that point already eliminated the ballot will be allocated to that candidate, otherwise the second preference is ignored, and the ballot’s third preference evaluated, and so-on… until the ballot is successfully allocated to a non-eliminated candidate, or until all the preferences expressed on the ballot have been exhausted.
  2. As soon as we get a candidate with a majority we stop, disregarding any further preferences.
  3. This means that voters’ full expressed preferences do not come into play in the IRV election decision. Lower preferences on any given ballot have no effect at all until or unless all higher-preference candidates on that given ballot have been eliminated, and then only if that lower-preference candidate is at that point not already eliminated and we have not yet found a majority winner.

There are notable other weaknesses in this system. For example: as for FPTP, “similar” candidates will tend to appeal to the same voter base. Such voters will tend to rate such candidates similarly, which will tend to spread support among them, reducing the individual standings of all such candidates in each round of counting, i.e.: “splitting” the “similar” vote, diminishing the prospects for them all.

This can cause such similar candidates to be eliminated, whereas one of them might otherwise have won.

Unlike FPTP, however, as similar candidates are eliminated their support will tend to be reallocated to the remaining “similar” candidates. If a candidate can survive the count until his or her similar competitors are eliminated, the problem works itself out – at least from the perspective of that surviving candidate!

Consider as well a situation where the first-preference last-place candidate though having fewer first-preference supporters is everyone-else’s second choice.

Looking at such a strong second-preference showing one could see, intuitively, that if there is no first-preference majority this last-place first-preference candidate might well be the candidate who in the end is “most preferred” across the board. But, being in last place on the first count he or she would be eliminated straight away.

IRV is sensitive to the order in which candidates are eliminated, which can affect which other candidates are eliminated and in what order.

Ranked Pairs and other Condorcet methods do NOT operate by “eliminating” candidates, and thus are not prey to this fault – all ballot preferences for all valid ballots come into play in determining the outcome.

The following example illustrates how a most-preferred candidate can be eliminated rather than elected, as well as the case where the least-preferred candidate is elected rather than eliminated. IRV is NOT a Condorcet method:

1. Winner-Loses Scenario

To demonstrate this let us imagine that we have four candidates: W, X, Y, Z, where W has relatively low first-preference support, but substantial support after that.

Let us imagine an election by preferrential ballot, where the voters record their preferences among these given candidates by voting 1 for first-preference, 2 for next-preference, and so on.

We then evaluate these cases in terms of first past the post (FPTP), Instant Runoff Voting (IRV), and any Condorcet method (there being no preference cycle in these results, a Condorcet-completion approach is not required).

2. FPTP and IRV Analysis

The following “as voted” table represents all possible permutations (excluding preferred-same-as scenarios) of voter preferences, along with vote counts contrived to demonstrate the point at hand:

Preferences: 1 2 3 4 Ballots
W 6.0% X 4.0% Y Z 2.0%
Z Y 2.0%
Y 0.0% X Z 0.0%
Z X 0.0%
Z 2.0% X Y 1.0%
Y X 1.0%
X 26.5% W 21.0% Y Z 11.5%
Z Y 9.5%
Y 3.5% W Z 2.5%
Z W 1.0%
Z 2.0% W Y 1.5%
Y W 0.5%
Y 33.5% W 20.5% X Z 10.5%
Z X 10.0%
X 3.0% W Z 5.0%
Z W 5.0%
Z 3.0% W X 2.0%
X W 1.0%
Z 34.0% W 20.0% X Y 10.0%
Y X 10.0%
X 10.0% W Z 5.0%
Z W 5.0%
Y 4.0% W X 2.0%
X W 2.0%
100.0% 100.0% 100.0%
  • By FPTP only the first preference on any ballot is used. Candidate Z, having the most first-preference ballots, wins — with 34% of the vote.
  • By IRV, there being no first-preference majority, we eliminate the lowest-score candidate, W, reallocating his or her ballots according to their next-preferences, and proceed to the second count:
    Candidate W is Eliminated, Ballots reallocated.
    Voter-preference Ignored, never used.

Upon eliminating candidate W and reallocating his or her ballots according to their next-preferences, we obtain the second-count result, as follows:

Preferences: 1 2 3 Ballots
X 30.5% Y Z 17.0%
Z Y 13.5%
Y 33.5% X Z 20.5%
Z X 13.0%
Z 36.0% X Y 21.0%
Y X 15.0%
100.0% 100.0%
  • There still being no majority, we eliminate the lowest-score candidate, X, reallocating his or her ballots according to their next-preferences, and proceed to the third count:
    Candidate X is Eliminated, Ballots reallocated.
    Voter-preference Ignored, never used.

Upon eliminating candidate X and reallocating his or her ballots according to their next-preferences, we obtain the third- and final-count result, as follows:

Preferences: 1 2 Ballots
Y Z 50.5%
Z Y 49.5%
100.0%
  • Having reallocated Candidate X‘s ballots, there is now a majority winner: Candidate Y wins by IRV on the third count.

3. Condorcet Analysis

The Condorcet tally for this scenario looks like this:

Candidate
Pairs
B more-
preferred
than A
No-
Preference
A more-
preferred
than B
Total
A: [candidate W]
vs
B: [candidate X]
49.5%
0.0%
50.5%
100.0%
A: [candidate W]
vs B: [candidate Y]
46.5%
0.0%
53.5%
100.0%
A: [candidate W]
vs B: [candidate Z]
45.0%
0.0%
55.0%
100.0%
A: [candidate X]
vs B: [candidate Y]
48.5%
0.0%
51.5%
100.0%
A: [candidate X]
vs B: [candidate Z]
49.0%
0.0%
51.0%
100.0%
A: [candidate Y]
vs B: [candidate Z]
49.5%
0.0%
50.5%
100.0%

  • The winner of each pairwise match-up is shown bold, and there are no preference cycles
  • W wins by majority in every pairing in which he or she occurs and is thus the Condorcet winner – by any Condorcet method – and is arguably the candidate “most preferred” by the electorate as a whole.
  • Similarly, candidate Z loses every pairing in which he or she occurs, and is thus the Condorcet loser – arguably the candidate “least preferred” by the electorate as a whole.

4. Comparative Results

Rank
FPTP
IRV
Condorcet
Remarks
1.
Z
Y
W
Winner
2.
Y
Z
X
3.
X
X
Y
4.
W
W
Z

Note that:

  • Candidate W, who wins by any Condorcet method, and is thus arguably the candidate most preferred by the voters, comes in dead last by both FPTP and IRV.
  • Candidate Z, who comes in dead last by any Condoret method, and is thus arguably the candidate least-preferred by the voters, wins by FPTP.
  • Candidate Y, who comes in next-to-last by any Condorcet method, wins by IRV.
  • Candidate rankings by FPTP vs Condorcet in this case are exactly the reverse of each other!

All systems have their own strengths and weaknesses; some are better than others in different ways, and this is true for preferential voting systems as well; nevertheless, I submit that the worst such preferential-voting system is still better than FPTP.

IRV isn’t the worst choice, despite its weaknesses. If our choice is only between IRV and FPTP, IRV is a good choice; but we can easily do better.

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