IRV - Sample election - favorite season

This article demonstrates the use of instant-runoff voting (IRV) on a small preference poll election to pick a majority winner among four candidates.

It also demonstrates the instability of IRV among elections with three strong candidates, and demonstrates how Condorcet method can pick a strongest majority winner without forced elimination.

Instant Runoff Voting uses rank preference ballots to allow a majority winner to be determined from one ballot from voters and a series of "instant" runoffs, eliminating one weakest candidate at a time until one candidate controls a majority of the votes.

Preference poll: Favorite Season

The poll included 76 voters from a summer camp in 2001. The poll question was chosen as favorite season to be easy for everyone to offer an opinion.

Ballot design and Voter demographics

Ballot layout

Here's the ballot layout used. Additional printed instructions merely included the sample ballot below, which is an exact reproduction of the used ballots, except for being marked.

Voter Demographics

     Instructions
     <P>
     Place an X in the first

     column by your first

     choice. You may also 

     offer different second

Notes:

• Voter ages were from 6 to 82.
• There was approximate equal male and females voting (30 males, 36 females)
• The groupings (under/over 40) were used to divide vote in two somewhat equal subgroups. (30 under age 40, and 35 age 40 or older)

Ballot markings

• All ballots were valid votes (one mark per rank placing), although some didn't follow directions exactly as the instructions requested.
• Markings
  • 58 marked X's (as requested)
  • 11 marked rank numbers 1,2,3 (in the proper columns)
  • 7 marked check-marks instead of X's
• Ranking depth:
  • 73 ranked three different choices
  • 1 ranked one choice
  • 1 ranked two choices
  • 1 ranked one choice repeated in all rankings (treated same as one choice)

Notes:

• 100% offered countable rank markings. This shows the concept of ranking preferences is natural and understandable with a simple example ballot.
• 97% of voters were willing and interested in offering more than one preference when allowed.

Election results

Voter subset results

Since the ballot included the voter's gender and age, majority favored seasons could be measured from different voter groups. After the election voters were grouped by two measures (Under 40, 40 or older), and (male, female).

Combinations of these categories allowed 8 voter subset polls. The winners did vary between voter subsets. In all cases except the full set of voters, the plurality winner (first round strongest candidate) was also the majority winner.

• Red show the plurality leader, while bold shows majority winners.
• For completeness, the above IRV process was advanced to the third round and two final candidates, even if a majority candidate was identified earlier.
• Results can be compared between different voter subsets and see how the votes combine to change the winners.
• Spring, Fall, and Summer all were favorites of different groups of voters. This demonstrates the existence of three strong candidates that may win the final round.

Full results

Summer was the plurality winner, while Spring was the majority winner, after a tie was broken.

     Females under 40:

     Spring wins both plurality and IRV.

     Males under 40:

     Summer wins a majority in round 1.

     Females 40 or older

     Spring wins both plurality and IRV.

     Males 40 or older

     Fall wins a majority in round 1.

     All Females

     Spring wins both plurality and IRV.

     All Males

     Summer wins both plurality and IRV.

     All younger than 40

     Summer wins both plurality and IRV.

     All 40 or older

     Plurality had a first place tie Fall/Spring

     IRV picked Fall

You'll notice this All-Voter election had a tie for last place in round two between Fall and Spring. This tie was broken by a rule that says "If there's a tie for elimination, eliminate the weaker candidate from the previous round." In this case Spring was stronger in the first round, so Fall is eliminated.

Counting

Process rules

Ballots were hand-counted.

Process:

• Ballots were piled by first choices
• Each pile was carefully counted and recorded.
• If one choice had a majority a winner was determined immediately.
• Otherwise the weakest choice was eliminated and that pile of ballots was redistributed to second choices.
  • Redistributed ballots can be piled next to the pile with the second choice so only the moved ballots need to be recounted.
• Repeat counts for each choice and repeat as needed.

Demonstration

This image shows the full-set election counting process. Ballots are piled by first rank choices in the first round, and transfer votes are placed next to existing piles until a majority winner is found in the third round. (Keeping transfer votes in parallel piles, rather than combining on old piles, reduces the work of counting, and keeping transfers piles separate makes it easier to resolve recount problems when identified.)

Missing image
Irvseasoncounting.png

Issue: Montonicity, tactical voting, and Condorcet's paradox

This example election is a good one to demonstrate the possibilities of paradoxical results that can occur within runoff systems.

The monotonicity criterion for voting systems is the following statement:

• If an alternative X loses, and the ballots are changed only by placing X in lower positions, without changing the relative position of other candidates, then X must still lose.

In this season election, Summer loses to Spring in the final round. However Spring was one vote away from elimination. The question Summer supporters might ask is "What would have happened if Fall had been ahead of Spring - Could Summer beat Fall?"

An IRV election can never answer this question because lower preferences that were not used are never counted.

To answer the hypothetical question of alternative results, we must go beyond IRV and look at the results from the Condorcet method which does not elimination candidates.

Condorcet's pairwise approach

The Condorcet method looks at pairwise competitions and if one candidate defeats all others pairwise, that candidate is called Condorcet's Winner.

The practical value of knowing the Condorcet winner within a IRV election is that if this candidate makes the final-two, this candidate is guaranteed to win against any competitor.

Below is the result from a Condorcet count in IRV round 3 for this favorite season election. Rounds 3a, 3b, 3c are "conditional" rounds, rather than actual elimination. They are done in parallel. Every voter gets one vote in each pair contest.

Tactical voting options in runoffs

Monotonicity is a principle that says that a candidate should not be able to lose votes and change from losing to winning.

Runoff elections can not guarantee this result when there are more than two strong candidates and the elimination order is unpredictable.

Voters may try to exploit this "feature" of runoffs using tactical voting to improve the chances for their candidate.

Specifically, Summer supporters have votes to spare at the first round. In this case, if one Summer supporter voted insincerely for Fall first instead that would help Spring be eliminated and then Summer would still have an easy win in the final round against Fall.

This is possible with enough pre-election polling information, and a close 3-way race, although still not easy in practice.

Tactical voting can be used even more easily in runoffs with multiple rounds of voting. If my candidate looks strong in the first round, and has two nearly equal opponents, I might attempt to vote for the more "polarized" opponent who has lots of core supporters, but less likely to gain compromise appeal in the final round. Then, if I succeed in a sequential runoff, I can happily move my final vote back to my favorite.

This strategic approach can also be used in party primaries. If my party has no competition, I might attempt to vote in the opposition party primary, try to help a strongly polarized candidate who is less likely to defeat my candidate in the general election.

However, Instant Runoff Voting makes this sort of strategic voting less effective since there's only one ballot and I can't play "bait-and-switch" between rounds. If I vote against my candidate in a rank ballot, I can't move back to my true favorite if my strategy succeeds. And there's a further danger if too many voters like me try this tactic, it might help a bad candidate win.

This election demonstrates the problems of runoff elections when there are more than two strong candidates. Runoffs can find "A majority winner", but that winner can change based on which candidate is eliminated first.

Some people judge that IRV is an inferior election method because it can not guarantee the monotonicity criterion. Supporters reply that it is a minor flaw that would happen rarely and it would be unlikely voters could exploit it to their benefit.

Supporter also point of that all election methods can have counterintuitive results in specific examples when allowing voters rank preferences among three or more choices. See Arrow's_impossibility_theorem

Condorcet's Paradox

Before you think that Condorcet's Pairwise approach may be a better way, consider that it is possible no pairwise winner exists. Among three, you might find cyclic preferences: Rock beats scissors, scissors beats paper, and paper beats rock.

This paradox can happen in Condorcet elections and must be dealt with before considering Condorcet's approach in a real election.

In fact such a cycle of preference occurred in the "All 40 or older" subelection above:

Here's that IRV election repeated, but stopping elimination in round 3 and allowing pairwise comparisons among all combinations.

     Peek at 

     alternatives

     ----->

     Condorcet

     Pairwise

     results:

• Fall beats Spring
• Spring beats Summer
• Summer beats Fall

• 79% (11/14) of Fall supporters liked Spring next.
• 77% (10/13) of Spring supporters liked Summer next.
• Summer supporters split equally: 4 moved to Spring, 4 moved to Fall.

Summary

IRV finds a majority winner

This example shows the ability of ranked preference ballots and IRV counting to determine a majority winner in one election through sequential elimination of candidates and recounting.

Plurality winners usually win runoffs as well

It shows that the plurality winner usually wins anyway, but majority support can be confirmed.

In this sample election: (And voter subgroup results)

• Only 2 of 9 elections had a majority winner in the first count.
• In 8 of 9 elections the plurality winner was confirmed by a majority with IRV.
• In 1 of 9 there was a last-place tie that required special rules to break it.

Ties must be dealt with

Last place ties for elimination are unlikely when there are many voters, but rules must be defined before the election to handle them.

Monotonicity of winners is not guaranteed

      Peek at 

     alternatives

     ----->

     Condorcet

     Pairwise