Ranked-choice Voting (also known as Single Transferable Vote)

Single Transferable Vote (STV) is the name that has been given to a category of ranked-choice voting (RCV, also known as preference voting) that elects more than one candidate per constituency.

In ranked-choice voting, each voter has the power of one vote, regardless of the number of seats to be filled. On the ballot, each voter ranks candidates in order of preference. The technique of tabulation is described at Wikipedia. Votes not used to elect one candidate on the list pass to the next.

To be elected, a candidate must receive a defined quota, based on the number of seats to be filled and the number of votes. The largest minority of voters whose votes will not be used is necessarily smaller than that threshold.

The Hagenbach-Bischoff quota is a number of ballots multiplied by the reciprocal of one more than the number of seats (equal to the number of ballots divided by one plus the number of seats). If that quota is used as the threshold a candidate must not merely reach but exceed, these are the fractions of all ballots that must be reached:

Number of seats to be elected in district Election thresholds in a multi-member district
measured as a portion of that district
for 1st seatfor 2nd seatfor 3nd seatfor 4th seatfor 5th seatfor 6th seatfor 7th seatfor 8th seatfor 9th seatfor 10th seatfor 11th seatfor 12th seat
1 1/2 50.0%
2 fs1/3 33.3% 66.7%
3 1/4 25.0% 50.0% 75.0%
4 1/5 20.0% 40.0% 60.0% 80.0%
5 1/6 16.7% 33.3% 50.0% 66.7% 83.3%
6 1/7 14.3% 28.6% 42.9% 57.1% 71.4% 85.7%
7 1/8 12.5% 25.0% 37.5% 50.0% 62.5% 75.0% 87.5%
8 1/9 11.1% 22.2% 33.3% 44.4% 55.6% 66.7% 77.8% 88.9%
9 1/10 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0%
10 1/11 9.1% 18.2% 27.3% 36.4% 45.5% 54.5% 63.6% 72.7% 81.8% 90.9%
11 1/12 8.3% 16.7% 25.0% 33.3% 41.7% 50.0% 58.3% 66.7% 75.0% 83.3% 91.7%
12 1/13 7.7% 15.4% 23.1% 30.8% 38.5% 46.2% 53.8% 61.5% 69.2% 76.9% 84.6% 92.3%

This chart shows how combining legislative seats into multi-member districts lends itself to ranked-choice voting (RCV):

Number of seats to be elected in district Election thresholds
measured as a quantity of seats
for 1st seatfor 2nd seatfor 3nd seatfor 4th seatfor 5th seatfor 6th seatfor 7th seatfor 8th seatfor 9th seatfor 10th seatfor 11th seatfor 12th seat
1 0.50
2 0.67 1.33
3 0.75 1.50 2.25
4 0.80 1.60 2.40 3.20
5 0.83 1.67 2.50 3.33 4.17
6 0.86 1.71 2.57 3.43 4.29 5.14
7 0.88 1.75 2.63 3.50 4.38 5.25 6.13
8 0.89 1.78 2.67 3.56 4.44 5.33 6.22 7.11
9 0.90 1.80 2.70 3.60 4.50 5.40 6.30 7.20 8.10
10 0.91 1.82 2.73 3.64 4.55 5.45 6.36 7.27 8.18 9.09
11 0.92 1.83 2.75 3.67 4.58 5.50 6.42 7.33 8.25 9.17 10.08
12 0.92 1.85 2.77 3.69 4.62 5.54 6.46 7.38 8.31 9.23 10.15 11.08


Dividing metropolitan areas

A chief complaint about clumsy districting is that it fragments press markets. If a district is in one large metropolitan area, the legislator must get coverage in that market. If a district includes an entire small metropolitan area among others, the reporters based there will have to cover the candidates in that district or run short of news to report. However, a legislator whose district has a small piece of a faraway place will find it difficult to get newspaper or TV attention there. Because there are more votes more easily obtained elsewhere, the gerrymander's tail is likely to be ignored, especially if it is home to only a small segment of voters in the news market. Without adequate press coverage, the voters who live in the gerrymander's tail lose their ability to make an informed choice.

To have the desired effect of increasing turnout, multi-member districts must enhance community cohesion. Another page explains how this might work in the state of Virginia.

District size

Not every size district is appropriate for multi-member districts. Because each district elects an integral number of legislators, it must be within the size range allowed for an integral number of seats.

2-member districts

A party can win one seat with 33.3% of the vote or two seats with 66.7%. Most contested legislative elections will produce enough votes for each major party to win one but not two seats. The vast majority of the time, the result of the vote will be predictable, removing the incentives for candidates to communicate and citizens to vote. There will be little publicity and poor turnout at the polls, just as now.

There are exceptions to the two-party split:

Single-party strongholds (pocket boroughs)
There are numerous demographically-skewed legislative districts where one party is so weak that the other wins nearly every election. The most visible examples are urban ghettoes where a legislator serves for decades without a serious challenge. Historically, though, there were vast parts of the South that only elected Democrats from the end of Reconstruction until the Voting Rights Act, about 87 years. The uniform poverty and powerlessness of the constituency prevents formation of a meaningful challenge to the incumbent. If the citizens became socially mobile and financially independent, they might threaten the incumbent's career. Despite the necessity to promise prosperity, the career legislator has a mighty incentive to keep it from being delivered to the home district.
In safe districts, the political minority tends to be small and permanently shut out. Bringing only two lopsided districts together is unlikely to make much difference, because a minority as large as 33.3% can still be shut out of an election. Greater aggregation is needed.

Independent insurgencies
Occasionally, an independent candidate bucks the two-party system and gets elected. Jesse Ventura's term as governor of Minnesota is a well-known example. Unfortunately, these strong independent insurgencies are rare. The personality of the candidate is usually the greatest driving factor. These candidates want quick results. They want to get their policies carried out without the horse-trading that pervades legislative work. Therefore, they tend to run for executive or statewide office, where they cam exercise power without wrestling career politicians daily. There are not enough of them to depend on to change the system.

Landslides in contested elections are the exception, not the rule. If they occur in multi-member districts, they tend to shut the minority out of participation, which is something election reform normally tries to change.
States with predictable results

This table shows vote for Congress in seven elections over the years 1996-2008, with STV (a form of RCV) awarding the same number of seats every time:

New Hampshire237.37% (2004)54.10% (2008)143.70% (2008)60.78% (2004)1
Utah326.87% (1998)42.92% (2006)151.30% (2006)64.62% (1998)2
Rhode Island and Providence Plantations211.21% (2006)29.93% (1996)0
New Mexico340.08% (2002)49.45% (1998)1
Mississippi441.88% (2008)59.00% (2004)2
Oklahoma554.58% (2002)64.53% (2000)3
Connecticut551.45% (2002)64.72% (2008)3
Oregon553.70% (2004)61.71% (2008)3
Wisconsin846.11% (2008)54.30% (2002)4
Michigan1543.93% (2008)49.42% (2004)7

Monotonicity failure

In 2002, N. R. Miller of the University of Maryland argued that preference (ranked-choice) voting fails the monotonicity criterion, defined by D. R. Woodall. According to the argument, raising the preference for a candidate (while holding constant the order of preference of other candidates) can cause that candidate to lose an election.

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Last revised: 24 February 2021