STV

Single Transferable Vote (STV) is the name given to a category of ranked-choice voting (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. 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 seat		for 2nd seat	for 3nd seat	for 4th seat	for 5th seat	for 6th seat	for 7th seat	for 8th seat	for 9th seat	for 10th seat	for 11th seat	for 12th seat
1	1/2	50.0%
2	1/3	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%

Number of seats to be elected in district	Election thresholds measured as a quantity of seats
	for 1st seat	for 2nd seat	for 3nd seat	for 4th seat	for 5th seat	for 6th seat	for 7th seat	for 8th seat	for 9th seat	for 10th seat	for 11th seat	for 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

Limitations

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. The voters who live there 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 67.7%. 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

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.

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

STATE		DEMOCRATIC CANDIDATES			REPUBLICAN CANDIDATES
NAME	SEATS IN CONGRESS	MINIMUM VOTE	MAXIMUM VOTE	SEATS WON EVERY TIME	MINIMUM VOTE	MAXIMUM VOTE	SEATS WON EVERY TIME
New Hampshire	2	37.37% (2004)	54.10% (2008)	1	43.70% (2008)	60.78% (2004)	1
Utah	3	26.87% (1998)	42.92% (2006)	1	51.30% (2006)	64.62% (1998)	2
Rhode Island and Providence Plantations	2				11.21% (2006)	29.93% (1996)	0
New Mexico	3				40.08% (2002)	49.45% (1998)	1
Mississippi	4				41.88% (2008)	59.00% (2004)	2
Oklahoma	5				54.58% (2002)	64.53% (2000)	3
Connecticut	5	51.45% (2002)	64.72% (2008)	3
Oregon	5	53.70% (2004)	61.71% (2008)	3
Wisconsin	8				46.11% (2008)	54.30% (2002)	4
Michigan	15				43.93% (2008)	49.42% (2004)	7

Monotonicity failure

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