Nonpartisan proportionality

For more information on the system, check out the real-life wikipedia page on the Single Transferable Vote.

Nonpartisan proportional voting (NPV), often called Proportional representation (PR), or commonly known IRL as Single Transferable Vote (STV) is a multi-winner electoral system in which voters cast a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to marked back-up preferences if their preferred candidate is eliminated, so that their vote is used to elect someone they prefer over others in the running.

NPV aims to provide proportional representation based on votes cast in the district where it is used, so that each vote is worth about the same as another. Unlike in single-winner and majoritarian systems as first-past-the-post (FPTP), instant-runoff voting (IRV; also known as the alternative vote), one party or voting bloc (such as towns or factions of a nation) can take all the seats in a given electorate. While under NPV that is highly unlikely, unless the number of seats is very small or almost all the votes cast are cast for one party or group's candidates. The key to NPV's approximation of proportionality is that each voter effectively only casts a single vote in a contest electing multiple winners, while the ranked ballots (and sufficiently large districts) allow the results to approach proportionality.

Under proportional representation, multiple winners are selected for an electoral district, however this district may constitute the entirety of a nation or other polity. Every sizeable group within the district wins at least one seat: the more seats the district has, the smaller the size of the group needed to elect a member. In this way, NPV provides approximately proportional representation, ensuring that substantial minority factions have some representation.

Proportional representation is distinguished from plurality voting systems, like FPTP, plurality block voting and the single non-transferable vote (SNTV) by the fact that votes are transferable under NPV but are not under the other systems. NPV reduces the number of "wasted" votes (votes which are cast for unsuccessful candidates and for successful candidates over and above those needed to secure a seat) by electing multiple representatives for a district. Additionally, surplus votes collected by successful candidates are transferred to aid other candidates.

An important characteristic of NPV is that it enables votes to be cast for individual candidates rather than for parties. Party lists are therefore not needed (as opposed to many other proportional electoral systems); it is the voters who create their own ordered list of candidates. The ranked voting also allows voters to form consensus behind the most popular candidates.

Nonpartisan proportional representation is used in all elections in the Republic of Cascadia, and were formally used in the Midwestern Union and Republic of British Columbia.

Process

On their ballot, the voter ranks candidates in order of preference. A vote is initially allocated to the voter's first preference. If seats remain open after this first count, votes are transferred as per following steps.

If that candidate is eliminated, the vote is transferred to the next-preferred candidate rather than being discarded; if the second choice is eliminated, the procedure is iterated to lower-ranked candidates. Under some systems, the vote is apportioned fractionally to different candidates. As long as there are more candidates than seats, the least popular candidate is eliminated, and votes for them are transferred based on voters' subsequent preferences.

Before the election, a quota (the minimum number of votes that guarantees election) is calculated by a specified method, and candidates who accumulate that many votes are declared elected. In some systems, the quota is also used to determine surplus votes, the amount of votes received by successful candidates over and above the quota. Surplus votes are transferred to candidates ranked lower in the voters’ preferences, so they would not be wasted by remaining with a candidate who does not need them.

Transfer of surplus votes is done before any eliminations of candidates. This prevents a party from losing candidates in the early stages who might be elected later through transfers.

Counting, eliminations, and vote transfers continue until enough candidates are declared elected (all seats are filled by candidates reaching the quota) or until there are only as many remaining candidates as there are unfilled seats, at which point the remaining candidates are declared elected. The specific method of transferring votes varies in different systems (see ).

District elections grow more proportionally representative in direct relation to the increase in the number of seats to be elected in a constituency more seats, the more the distribution of the seats in a district will be proportional. For example, in a three-seat NPV election using the Hare quota of valid votes casts / seats to fill, a candidate or party with 33 percent of the votes is guaranteed to win a seat. In a seven-seat proportional contest using the Hare quota, any candidate with approximately 14 percent of the vote (either first preferences alone, or a combination of first preferences and lower-ranked preferences transferred from other candidates) will win a seat. Many systems use the Droop quota, which is even smaller than the Hare for the same number of seats.

Because of this quota-based fairness, under NPV it is extremely rare for a party to take a majority of the seats in a district without a majority of the district vote. Additionally, a large majority of voters (generally around 80 percent or more) see their vote used to elect someone. Thus under NPV, the candidates who make up a majority of the district's elected members are supported directly by a majority of the voters in the district.

Example for a non-partisan election

Suppose an election is conducted to determine what three foods to serve at a party. There are seven choices: Oranges, Pears, Strawberries, Cake (Strawberry-chocolate), Chocolate, Hamburgers and Chicken. Only three of these may be served.

There are 23 guests, and the hope is that each guest will be served at least one food that they are happy with. It is decided to use NPV to make the decision. Each guest is given one vote but is also allowed to cast two optional alternate preferences to be used only if the first preference cannot select a food or to direct transfer of surplus votes if it does. The 23 guests at the party mark their ballots: some mark first, second and third preferences; some mark fewer preferences. When the ballots are counted, it is found that the ballots are marked in seven distinct combinations, as shown in the table below:

1st preference	Orange	Pear	Strawberry	Cake	Chocolate	Hamburger	Chicken
2nd preference	Pear	Strawberry	Cake	Chocolate	Cake		Hamburger
3rd preference		Cake	Pear	Strawberry	Hamburger
# of ballots	4	7	1	3	1	4	3

The table is read as columns: the left-most column shows that there were four ballots with Orange as the first choice, and Pear as second; while the rightmost column shows there were three ballots with Chicken as first choice and Hamburger second.

The election step-by-step:

Step	Votes for each option
	Orange	Pear	Strawberry	Cake	Chocolate	Hamburger	Chicken
Setting the quota	The quota is 6
Step 1	4	7 ELECTED (1 surplus vote)	1	3	1	4	3
Step 2	4	ELECTED	1 + 1 = 2	3	1	4	3
Step 3	4	ELECTED	2	3 + 1 = 4	eliminated	4	3
Step 4	4	ELECTED	eliminated	4 + 2 = 6 ELECTED (0 surplus votes)	eliminated	4	3
Step 5	4	ELECTED	eliminated	ELECTED	eliminated	4 + 3 = 7 ELECTED (1 surplus vote)	eliminated
Result		ELECTED		ELECTED		ELECTED

Setting the quota: The Droop quota formula is used, giving Quota = total votes / (options to choose + 1) + 1, rounded down = 23 / (3 +1) + 1 rounded down = 6.75 rounded down = 6

Step 1: First-preference votes are counted. Pears reaches the quota with 7 votes, and is therefore elected on the first count, with 1 surplus vote

Step 2: All of the voters who gave first preference to Pears preferred Strawberry next, so the surplus vote is awarded to Strawberry. No other option has reached the quota, and there are still two to elect with six options in the race, so elimination of lower-scoring options will start on the next round.

Step 3: Chocolate has the least votes and is eliminated. According to their only voter's next preference, this vote is transferred to Cake. No option has reached the quota, and there are still two to elect with five in the race, so elimination of options will continue next round.

Step 4: Of the remaining options, Strawberry now has the least votes and is eliminated. In accordance to the preferences of both the only voter who voted Strawberry, and the Pear–Strawberry–Cake vote, these votes are transferred to Cake. Cake reaches the quota and is elected. No other option has reached the quota, and there is still one to elect with three in the race, so elimination of options will continue next round.

Step 5: Chicken has the least votes and is eliminated. According to the Chicken voters' next preference, this vote is transferred to Hamburgers. Hamburgers is thus elected with 7 votes in total. Hamburgers now also has a surplus vote, but this does not matter, since the election is over. There are no more foods needing to be chosen - three have been chosen.

Result: The winners are Pears, Cake, and Hamburgers.

NPV in this case produced a higher number of effective votes - 19 votes were used to elect the successful candidates. (Only the votes placed for Oranges were neither used to select a food nor transferred.) As well, there was general satisfaction with the choices selected 14 voters saw their first preference chosen, and the 9 others saw their second preference chosen. In addition, seven saw their first and third choices selected; one saw his second and third choice selected.

Note that if Hamburger had received only one vote when Chicken was eliminated, it still would have won because the only other remaining candidate, Oranges, has fewer votes so would have been eliminated in the next round. This would have left Hamburger as the last remaining candidate to fill the last open seat, even if it did not have quota.

Compared to other systems

This result differs from the one that would have occurred if the voting system used had been non-PR, such as single non-transferable vote (SNTV), first-past-the-post (FPTP) in three districts, or at-large block voting.

Single non-transferable vote results would have had Orange among the three winners, as opposed to Cake, for having a greater number of first-preference votes. Under SNTV, 15 voters would have seen their first preference win (Oranges, Pears and Hamburgers); only 3 voters would have not seen their first preference food served but would have seen their 2nd preference food served. Five voters would not be served any of their favorites.

Under first-past-the-post, the guests would have been split into three groups with one food chosen by each group based on just the most popular food in each group. The result in this case would have been dependent on how the groups are formed (gerrymandering of the groups to bias the election toward a particular result could also occur). It might have been Strawberry donuts, Pears and Hamburgers, but also the foods chosen might have been Pears in two groups (districts) and Hamburgers in the other. Or even just Pears alone might have won in each of the three "districts", in which case only 7 guests out of 23 would have seen their first choice served, a very unrepresentative outcome, given that three different foods could have been served.

Similar problems arise to a lesser degree if all districts use a majority system instead of plurality (for instance, two-round or instant-runoff voting) as at least in all districts the majority would have been quite happy, but that still leaves the minority unrepresented.

It could happen under any three-district single-winner system that none of the groups elect Pears, if the 7 votes for it are split and in each "district" there is another food that beats it (e.g. Oranges, Hamburgers and Chicken).

If the voters had been able to choose only one food to serve (as in first-past-the-post, but without "districts"), it is likely that Pears, the choice of less than a third of the 23 party-goers, would have won, meaning Pears would be the only food served at the party. Even if they held two rounds of voting, the bare majority that prefers some kind of fruit (Oranges, Pears, Strawberries) would have dominated all other choices.

Giving electors a transferable vote is very different from simply giving each voter more votes to cast. At-large block voting is such a system. Under it, each voter is given as many votes as there can be winners. This system can produce very unrepresentative results. In the example above, if every voter could vote for three options, the small majority of voters who chose a fruit could easily force all three outcomes to be fruit of some kind: an outcome that is unlikely to be more representative than simply choosing only one winner. In an extreme example, where no faction can command an absolute majority, the largest of the minority groups can force a one-outcome result by running clone candidates. For example, the seven supporters of Pears could arrange in advance to have three types of Pears included on the ballot, then vote for all three, and if no other option reaches more than 7 votes, all three foods would be a type of Pear. The only way this could be avoided would be for those who do not want Pears to vote tactically by not choosing their preferred option, but instead whatever they consider to be the least bad outcome that is still likely to gain the required number of votes.

Example for an election with parties

Elections with parties are conducted in very similar manner to the non-partisan proportional election presented above. Parties actually play no role in NPV elections – each voter marks preferences for individual candidates and his or her secondary preferences may cross party lines if so desired.

This example shows election of five members in a district. Party A runs five candidates, Party B runs three, and there is one independent in the race. The election is conducted under Proportional Voting with the Hare quota, which for five seats is 20% (100% divided by five).

First round

Candidate	Party		Votes (first preferences)	Quota	Elected?	If elected: surplus votes
Candidate A1		Party A	1%	20%
Candidate A2		Party A	9%
Candidate A3		Party A	25%		Yes	5%
Candidate A4		Party A	8%
Candidate A5		Party A	5%
Candidate I		Independent	7%
Candidate B1		Party B	11%
Candidate B2		Party B	18%
Candidate B3		Party B	16%
TOTAL			100%

In the first round, the vote tally of the most popular candidate of Party A, Candidate A3, is more than quota, so they win a seat.

Second, third and fourth rounds

Surplus votes are distributed; the voters of Candidate A3 have put another politician from their party, Candidate A4, as their second preference, so A4 now receives Candidate A3's surplus votes. This transfer of 5 percent of the votes leaves A3 with the quota (20 percent) and leaves A4 with 13 percent.

In the third and fourth rounds, the least popular candidates are eliminated (Candidates A1 and A5) and their votes transferred to their next preferences. Voters of Candidate A5 are not very partisan, they actually prefer the independent candidate over the other candidates of Party A still in the race.

Candidate	Party		Votes	Quota	Elected?	If elected: surplus votes
Candidate A1		Party A	1% − 1% = 0%	20%
Candidate A2		Party A	9% + 1% = 10%
Candidate A3		Party A	25% − 5% = 20%		Yes	already elected
Candidate A4		Party A	8% + 5% = 13%
Candidate A5		Party A	5% − 5% = 0%
Candidate I		Independent	7% + 5% = 12%
Candidate B1		Party B	11%
Candidate B2		Party B	18%
Candidate B3		Party B	16%
TOTAL			80% (1 already elected)

Fifth and sixth rounds

In the fifth round, Candidate A2 is eliminated with all their votes going to the candidate A4, the last remaining candidate from Party A, who is elected. The surplus votes of Candidate A4 are transferred. All the voters who helped elect Candidate A4 prefer the independent candidate to the candidates of the other party so their 3% surplus votes will go to Candidate I in the sixth round.

Candidate	Party		Votes	Quota	Elected?	If elected: surplus votes
Candidate A1		Party A		20%
Candidate A2		Party A	10% − 10% = 0%
Candidate A3		Party A	already elected		Yes
Candidate A4		Party A	13% + 10% = 23%		Yes	3%
Candidate A5		Party A
Candidate I		Independent	12% + 3% = 15%
Candidate B1		Party B	11%
Candidate B2		Party B	18%
Candidate B3		Party B	16%
TOTAL			80% (1 already elected)

Seventh round

There are now only four candidates remaining and three seats remaining open. The least popular candidate (Candidate B1) is eliminated. There are now only three candidates in the race, so they are automatically declared elected regardless of whether they reached the quota. If there is no reason to establish relative popularity of the elected members, the count ends there when the last seats are declared filled.

If the ranking of the candidates is important, the votes belonging to Candidate B1 might be transferred as per below, assuming voters' alternate preferences are marked that way.

Candidate	Party		Votes	Quota	Elected?	If elected: surplus votes
Candidate A1		Party A		20%
Candidate A2		Party A
Candidate A3		Party A	already elected		Yes
Candidate A4		Party A	already elected		Yes
Candidate A5		Party A
Candidate I		Independent	15% + 5% = 20%		Yes
Candidate B1		Party B	11% − 11% = 0%
Candidate B2		Party B	18% + 6% = 24%		Yes
Candidate B3		Party B	16%		Yes
TOTAL			60% (2 already elected)

Under nonpartisan proportional voting, candidates A3, A4, I, B2 and B3 were elected.

This vote count varies from the reality of many NPV systems because there were no "exhausted" non-transferable votes. In most real-life NPV elections, some votes that are set to be transferred cannot be and the number of votes still in play at the end is lower than the number of votes cast and counted in the 1st round. As well, the Droop quota is usually used in real-life NPV elections. With the Droop quota in effect and five seats, it would have taken 17 percent to be elected with quota, not 20 percent as under the Hare quota.

In this case, as in all NPV elections, about 80 percent or more of the votes were used to actually elect someone. A majority of the members elected in the district represent the sentiments of a majority of the voters.

Compared to other systems

This result differs from the one that would have occurred if the voting system used had been non-PR, such as single non-transferable vote (SNTV), first-past-the-post (FPTP) in five districts, or at-large block voting.

This result is different than if all voters could only vote for their first preference, which is called the single non-transferable vote. Under SNTV, the five candidates most popular when only first preferences are considered were candidates A2, A3, B1, B2 and B3. This means even though Party B's candidates had less support together, they would have received 60% of seats, and Party A only 40%. In this case, Party A overextended themselves by fielding too many candidates, but even if they had strategically nominated only three, they would not necessarily have been successful in gaining three seats instead of two seats, because one or two of their candidates might have taken the lion share of their party votes, leaving not enough for the other(s) to be elected. This could be addressed under SNTV if the party voters used coordinated strategic voting.

If voters could vote for five candidates (but not cast ranked votes) as under the plurality block voting system, a type of multiple non-transferable vote, Party A could have won all seats, leaving Party B and voters of the independent candidate without representation. This is because if all voters of Party A voted for all five of the Party A candidates, every Party A candidate would have been among the five candidates with the most votes and would have been declared elected. That would have meant that Party A with support of only 48 percent of voters would have had all the representation.

Under majority block voting, if voters voted along party lines, every Party A candidate would have received a vote from 48 percent of the voters, and some even up to 55% if voters of Candidate I also voted for some Party A candidates with their 4 other votes. At the same time, Party B's candidates could only get up to 52% of the votes with the same tactics. If the voters are partisan enough, the likely outcome is that party A would take all the seats although Party A took less than half the votes (minority representation) and all other votes are wasted.

In single-winner systems, whether First past the post or majoritarian, the outcome is uncertain. It likely would be that Party A with 48 percent of the votes might achieve a clean sweep of all five seats or easily Party A might take four of the five with Party B taking just one. (The first case would have been achieved by Party B votes being cracked by the district boundaries; the second case would have been achieved by Party B voters being mostly packed into just one district, leaving Party A with easy victories in the other four districts.) On the other hand if districts were drawn in different fashion, Party A and Party B might have divided the seats in a three to two ratio. Even under certain circumstances, the Independent candidate might take a seat if their supporters are sufficiently concentrated in one district.

NPV election results are roughly proportional (as much as the number of seats allows) and take into account more than the first preferences of voters. Under NPV (as seen in the example above), when it comes to secondary preferences, some voters who like a candidate from a certain party best might prefer an independent (or even a rival party candidate) before other candidates of their first choice's party. This means that even if it seems that some faction (based on first preferences) is over-represented or under-represented in the outcome, the outcome actually closely adheres to a combination of the first preferences of many voters and secondary preferences of most of the other voters. Under NPV, about 80 percent of voters see their vote actually used to elect someone they prefer (and even more than that portion see someone they prefer elected even if their vote itself was not used to elect anyone), while under FPTP, often less than half of the votes are used to elect anyone and only the largest group in each district is represented.

Party		Popular vote	NPV - Hare		SNTV		At-large Block		Party List
		%	Seats	%	Seats	%	Seats	%	Seats	%
	Party A	48%	2	40%	2	40%	5	100%	3	60%
	Party B	45%	2	40%	3	60%	0	0%	2	40%
	Independent	7%	1	20%	0	0%	0	0%	0	0%

Related voting systems

Instant-runoff voting (IRV) is the single-winner analogue of NPV. It is also called "single-winner ranked-choice voting". Its goal is representation of a majority of the voters in a district by a single official, as opposed to NPV's goals of not only the representation of a majority of voters through the election of multiple officials but also of proportional representation of all the substantial voting blocks in the district.

Two-vote MMP and additional member system systems may also be interpreted as a related, effectively preferential mixed system, but the vote transfer mechanism as under NPV does not exist in it or plays a minor role.

The modified d'Hondt electoral system is a variant of NPV, where an electoral threshold for parties is applied.

Terminology

In real life, it is often referred to as Single Transferable Voting, or STV. Other terms include Relative proportionality, Ranked choice proportionality, among others.

Balloting

In NPV, each voter casts just one vote although multiple seats are to be filled in the district. Voters mark first preference and can provide alternate preferences to be used if needed. In practice, the candidates' names are usually organized in columns so that voters are informed of the candidates' party affiliations or whether they are standing as independents.

They may indicate their preferences by ranking the candidates in order of preference. They would use ordinal numbers (1. 2. 3. etc.) to show this.

An alternative way to mark preferences for candidates is to use columns for the voters' preference with the name of each candidate appearing in each column. The first column is used to indicate first preference. An X there goes beside the most preferred candidate. The next column is for the second preference. An X there marks the second-preference candidate, etc.

Seat filling by quota

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In most NPV elections, a quota is established to ensure that all elected candidates are elected with approximately equal numbers of votes. In some NPV varieties, votes are totalled, and a quota (the minimum number of votes that guarantees election) is derived. Those who are elected are the most popular so quota does not affect that. Some say that the importance of quota is to set the amount of votes that are surplus, the amount that should be transferred away from successful candidates.

In some implementations, a quota is simply set by law - a candidate receiving a given number of votes is declared elected, with surplus transferred away. Something like this system was used in real-life New York City from 1937 to 1947. Under such a system, the number of representatives elected varies from election to election with voter turnout. In the 1937 New York City Council election 26 councillors were elected; in 1939 New York City Council election, newspapers reported that it was expected that the number of councillors would drop to 17 due to lower voter turnout.

A more common formula sets quota as a percentage of the votes cast. A four-seat district using the Hare quota sets quota as 25 percent of the valid votes; a four-seat district using the Droop quota sets the quota as one more than 20 percent of the valid votes.

Once a quota is determined, candidates' vote tallies are consulted. If at any time a candidate achieves the quota, they are declared elected. Then if there are still unfilled seats, in some NPV systems, any surplus votes (those over and above the quota) are transferred to other candidates in proportion to the next-highest preference marked on the ballots received by that candidate, if any.

Usually one or more candidates achieve quota in the first count. If there are still unfilled seats after the surplus is transferred, the count would proceed with the candidate with the fewest votes being eliminated. Their votes would be transferred to other candidates as determined by those voters' next preference, if any. Elections and eliminations, and vote transfers where applicable, continue until enough candidates are declared elected to fill the open seats or until there are only as many remaining candidates as there are unfilled seats, at which point the remaining candidates are declared elected. These last candidates may be elected without surpassing quota, but their survival until the end is taken as proof of their general acceptability by the voters.

List of users on EMC

NPV is used in several nations on EMC.

National legislatures

The table below lists countries that use proportional representation to fill a nationally elected legislative body by direct elections.

Country	Body	Type of body	Quota	Constituencies	District magnitude	Governmental system	Since	Notes
Cascadia	House of Representatives	Unicameral legislature	Droop quota	Electoral divisions	3–5	Presidential system	September 17, 2022	Prior to using proportional representation a version of score voting was used.
British Columbia	Senate	Unicameral legislature	Droop quota	None. At-large.	3	Directorial system	TBA
Midwestern Union	Congress of the Union	Unicameral legislature	Droop quota	States and territories of the Midwestern Union	2–7	Presidential system	Mid-2022	The Congress was a bicameral legislature for a brief period near the founding of the Republic; the House was elected by Proportional representation, while the Senate was not.

Benefits

Advocates for NPV argue it is an improvement over winner-take-all non-proportional voting systems such as first-past-the-post, where vote splits commonly result in a majority of voters electing no one and the successful candidate having support from just a minority of the district voters. NPV prevents in most cases one party taking all the seats and in its thinning out of the candidates in the field prevents the election of an extreme candidate or party or group if it does not have enough overall general appeal.