Multiple-Seat Delegative Elections

Bryan Ford - October 21, 2002


Single-Winner Elections

Multiple-Seat Elections

(Copyright 2002 Bryan Ford)

Seats and Districts

Multiple-seat elections are used for deliberative bodies such as congresses, parliaments, or councils, which are usually intended to be representative of some larger electorate. There is a tremendous variety of methods by which such bodies can be elected, but most schemes involve dividing the electorate up into districts along some more-or-less arbitrary lines, usually on a geographic basis, so that each district represents an approximately equal number of voters and is responsible for electing a given number of seats on the council. Districting effectively divides the election of the body a priori into several smaller elections for different parts of the council.

In common single-member plurality (SMP) systems such as those used in the U.S. and Britain, each district is represented by one seat on the body, and each district uses simple plurality voting to elect a representative to that seat. Unfortunately, this approach is fraught with problems. First, since the representative for each district is elected in a single-winner plurality election, these elections are vulnerable to spoilers, wasted votes, and election of representatives with less than majority support in the same way that other single-winner plurality elections are vulnerable. Second, SMP often produces highly disproportional results: for example, large minority groups that are dispersed among multiple districts, as racial and ethnic groups often tend to be, often find themselves with little or no representation whatsoever because their votes do not constitute a majority in any one district. Third, the traditional approach is highly vulnerable to gerrymandering, or explicit manipulation of the boundaries of districts by leaders in power - effectively "choosing their voters before the voters can choose them" - so as to help their party or strengthen their positions as incumbents.

Delegative voting can be used to elect candidates to representative bodies using many single-seat districts, a smaller number of multiple-seat districts, or even all at once in "one big district". Using DV with single-member districts brings with it the same advantages as other single-winner DV elections do over single-winner plurality elections, but single-member DV can still produce highly disproportionate results across the overall resulting body, and is still susceptible to gerrymandering. Using DV to elect multiple seats at once produces much more proportional results and is less susceptible to gerrymandering; using DV to elect the entire body at once ensures extremely proportional results and is not vulnerable to gerrymandering at all because there are no districts to manipulate. Furthermore, DV is the only proportional representation system known that can make it realistically both viable and compelling to elect large bodies with hundreds or thousands of seats, potentially representing millions or hundreds of millions of electors, in a single election consisting of just one enormous district.

How it works

In a multi-seat delegative election, each candidate for a given district decides and registers a next-choice list well before the election, exactly as in single-winner DV. Votes are similarly taken and counted exactly as in single-winner DV: each voter indicates a choice for a single candidate, and the primary result from the counting process is simply a table indicating the total number of votes received by each candidate. This raw table of results can then be made publicly available and widely distributed.

To determine which candidates actually win seats in the election, a quota is calculated based on the number of seats in the district and the total number of valid votes received by all candidates. This quota is calculated as follows:

quota =
number of votes
(number of candidates + 1)
+ 1

The list of candidates is then sorted according to the number of votes each received, and the list is progressively shortened by either electing or eliminating one candidate at a time. At each step, if the candidate with the most votes has exceeded the quota, then that candidate is awarded a seat, removed from the list, and any surplus votes the candidate received above the quota are transferred according to his established next-choice list. If on the other hand no candidate has reached the quota, then the candidate with the fewest votes is eliminated and his votes are similarly transferred according to his next-choice list. As with single-winner DV, votes to be transferred are divided equally between all the candidates on the next-choice list that have not yet been elected or eliminated. This process continues until all seats have been filled or there enough seats available for all remaining candidates.


Multi-seat DV provides the same advantages as single-seat DV in that it avoids wasted votes and spoilers, and it promotes a broader effective choice of candidates by giving parties or candidates that are too small to win seats themselves the power to affect the outcome of the election indirectly and thereby achieve some degree of influence. Furthermore, multi-seat DV yields extremely proportional results within a given district. A group commanding a given percentage of the popular vote in a district is guaranteed to be able to determine that percentage of the district's seats on the council, rounded down to the nearest seat. A group representing majority in the district will command a majority on the council as well. The level of proportionality of results across all the districts electing a body of representatives, of course, depends on the number of seats in each district: larger districts tend to produce more proportional results.

Relationship to Single Transferable Vote

In the same way that single-winner DV is really just a variant of IRV, multi-seat DV is actually just a variant of Single Transferable Vote (STV). Multi-seat DV uses essentially the same selection and elimination process as STV to determine the winning candidates, except that, as with single-winner DV, the way a particular vote is transferred is determined by the voter's first-choice candidate, rather than by an explicit ranking on the ballot itself. For this reason, multi-seat DV has exactly the same apparent drawback with respect to STV as single-winner DV does with respect to IRV: given a fixed number of candidates, voters have somewhat less flexibility in indicating their preferences. On the other hand, multi-seat DV also has exactly the same set of advantages over STV, such as simplicity, transparency, cost, speed, security, and potentially an even broader spectrum of candidates to choose from.

Furthermore, the simplicity, speed, and cost advantages of DV are even more profound for multi-seat elections than they are for single-winner elections, because multi-seat STV elections are inherently more complex and usually involve a much larger number of vote transfers before the complete outcome of the election can be determined. The process of electing and eliminating candidates and repeatedly re-shuffling their ballots according to successive choices can go on for days even if districts are kept fairly small. In DV, on the other hand, counting ballots is just as quick and easy as it is in plurality systems; once the raw tallies for all the candidates are available, determining the winners can be done manually in a matter of minutes or automatically in a matter of seconds by a simple computer program. Further, this program could be widely distributed along with the raw totals so that the election results can be independently verified by anyone.

Beyond these advantages, DV has one additional advantage over STV that is unique to multi-seat elections. In STV, the transfer of a candidate's surplus votes, after the candidate has exceeded the quota and been awarded a seat, presents a problem: exactly which of the candidate's ballots should be transferred and which should be set aside to fill the quota? In STV, this question matters at least in theory if not necessarily in practice, because different ballots that wind up in one candidate's pile can have different next-choice lists. If your particular ballot happens to be selected for transfer, then your ballot has a chance of affecting the election of other candidates; if your ballot is one of the ones set aside to fill the quota, then it is "dead" and cannot have any further effect. Simply picking an arbitrary set of ballots, such as by taking the appropriate number from the top of the candidate's pile, might give voters who voted earlier (or later) a better chance for their next-choices to influence the election. But taking special care to select a "random" sample, let alone examining all the ballots and ensuring that the set selected for transfer is properly "representative" of all the ballots by some definition of "representative", is more difficult and is probably only practical if the counting process is fully automated. In contrast, delegative voting sidesteps this issue entirely because all of the ballots for a given candidate are inherently identical and indistinguishable: only numbers have to be shuffled and reshuffled, not ballots.

The Single-District Ideal

When Thomas Hare first developed the STV system in the 19th century, he proposed treating the UK as one vast constituency, so that any voter in the country could vote for any candidate for the House of Commons regardless of geographic location. This approach would theoretically provide voters with the broadest possible choice of candidates, and would also ensure the most proportional possible results.

Obviously Hare's proposal was never adopted, and in practice STV has only been used either for electing fairly small bodies, such as the 9-member city council of Cambridge, Massachusetts, or by dividing a large body into constituencies with only a few seats each, such as Northern Ireland which uses constituencies of three to five seats. There are a number of reasons for keeping constituency sizes small:

  • Probably the most important reason is simply to keep the preferential ballots to a manageable size. Experience with STV shows that voters can manage to find and mark preferences for their favorite candidates among, say, a list of 10-20 candidates for a 5-seat district. The prospect of printing ballots listing hundreds or thousands of candidates for a single constituency, let alone expecting ordinary voters to find and mark preferences for their favorite candidates on such a list, is clearly unrealistic.
  • A second practical reason for small constitutencies is to keep the process of counting ballots manageable. With many small constituencies, the ballot counting process after an election can proceed independently and in parallel at various administrative centers throughout a country. But as long as ballots are physical pieces of paper, it would be very difficult to implement the STV counting process in a distributed fashion for one huge constituency; all the ballots cast throughout the entire country would instead probably have to be shipped to one central location, which might take weeks or months to count them all. Of course, automated ballot counting and electronic voting could substantially alleviate this problem, but not until standardized, interoperable automated systems have been pervasively deployed throughout the country, and even in the richest countries this condition is far from being met. Implementing large STV constituencies in a developing country would be out of the question (even ignoring the fact that implementing any preferential system in a country with substantial illiteracy and innumeracy is a highly dubious proposition in the first place).
  • A final reason sometimes cited for keeping constituencies small is to encourage candidates to be responsive to their local electorate. However, this argument only really holds water for List-PR systems, because they are party-based rather than candidate-based. Both STV and DV allow for highly effective constituency-based politics, as the discussion below will show.
Under multi-seat delegative voting all of the above problems become solvable. Because DV only requires voters to select a single candidate rather than to indicate an order of preference between several candidates, addressing the first problem above becomes merely a matter of choosing an appropriate balloting method. Voters in the U.S. are accustomed to ballots being pieces of paper printed by the state and listing all the official candidates for each office, which they must mark or punch before depositing into the box. An alternate approach, which has been well proven in the context of other electoral systems such as France's two-round system, is to have the candidates and parties themselves print their own ballots. The electoral authority specifies certain aspects of the ballot papers, such as their overall size and shape, but within these parameters the candidates and parties are free to design the ballots as they wish. Each ballot paper lists only a single candidate, perhaps along with other associated information such as party, slogan, or contact information - much like a business card. At election time, the voter selects a ballot paper from the desired candidate, inserts it in an envelope provided at the voting location, and drops the envelope into the ballot box. (The envelope serves to validate the ballot: only envelopes containing exactly one ballot will be counted, and any ballots found "loose" in the ballot box are discarded.)

With this voting mechanism, voters never need to worry about finding a desired candidate in a list of all possible candidates in a large multi-seat DV election. Instead, candidates can pass out their ballot cards through whatever channels they choose: in person, by mail, through the help of volunteers going door-to-door, or through the help of sympathetic organizations such as social, environmental, or religious groups. In addition, to ensure that every voter who shows up at a voting location always has several choices at election time even if they had no opportunity to receive ballot cards directly from candidates (or if they lost their cards), each official party would be allowed to provide a stock of ballot cards, to be made directly available at the voting location on election day, for one particular candidate selected by that party as the "default" candidate for that voting location. Thus, each voter can vote for any candidate they have received a card from directly, or can place a local "party-line" vote simply by showing up and picking a card from the appropriate party's stock of default ballots at their voting location.

In this system, candidates would have tremendous flexibility in choosing how to campaign. Many candidates would naturally focus on a particular local community - particularly those candidates selected by their affiliated parties to be the "default" candidate for corresponding voting locations. Such "geographic" candidates could ultimately determine their own geographic districts - e.g., which regions to focus on in their campaigns. Some candidates might attempt to campaign directly across a large region, in order to get as many direct votes as possible from the whole region. However, well-organized parties are likely to find it desirable to run a large number of candidates each covering fairly small regions, so that each of these candidates can cover her own area most effectively and even develop personal relationships with her constituents. This "saturation" could be highly effective even if the party ends up running far more candidates than can remotely be expected to win seats, because DV allows the smaller candidates to transfer their votes to the more popular or established candidates in the party, demanding in return the political attention and consideration of the larger candidates who do win seats, effectively allowing small candidates to become political proxies between the larger candidates and particular local communities. Other candidates might eschew geographic boundaries entirely and campaign within widely dispersed special interest groups, such as by mail, electronically, or by contacting voters and handing out their ballot cards at conferences related to their particularly community of interest. In effect, by avoiding the a priori establishment of arbitrary district boundaries, DV potentially allows the electors in to define their own "virtual constituencies" by virtue of the communities in which they choose to campaign.

Thus, the first problem above - providing voters with a practical way to select between a (theoretically) extremely large number of candidates - is solved. Solving the second problem, actually counting the ballots efficiently, also becomes relatively straightforward under DV. Since the only information needed from the counting process is the total number of votes cast for each candidate throughout the whole election, each voting location can count its ballots independently. Although each voting location could encounter a large variety of ballot papers in its ballot box, most of the ballots are likely to be for a few locally-popular candicates, so the counting process can be expected to proceed fairly quickly. Counting could be further sped by requiring the parties to include a bar code or other machine-readable label on their ballot papers. Each voting location, having counted the ballots cast at that location, then submit its raw numeric totals for each candidate to a central authority, which then simply combines the totals from all the voting locations to generate a final master list. Even if this master list contains vote counts for thousands or even millions of candidates, determining the winners of the election from this list (and from a database containing all of the candidates' next-choice lists) is still a straightforward computation that can be expected to finish in a matter of seconds.

In this way, all three major problems with large constituencies are solved, making DV apparently the first multi-seat electoral system that can realistically provide fully proportional district-free representation for bodies and electorates of essentially unlimited size. With single-constituency DV all cohesive parties and interest groups in the electorate can achieve representation in direct proportion to their size, completely independently of how concentrated or dispersed they may be. Further, there is no opportunity for gerrymandering since there are no districts to manipulate. Finally, since the only votes that are typically "wasted" in a DV election are votes that wind up with the last candidate to be eliminated, and this number is always less than the quota, the maximum possible fraction of "wasted" votes in the election decreases rapidly as the number of seats increases. Contrast this situation with SMP systems, where half or more of the votes in each district is ultimately wasted - and all of the votes in those districts that are "locked up" through natural demographics or gerrymandering - and it appears DV could provide a powerful tool for increasing the fairness of representation and in turn the effectiveness of a democracy.