Comparison of electoral systems
s are the rules for conducting elections. Comparisons between different systems can focus on different aspects: on suffrage or rules for voter eligibility; on candidate eligibility and the rules governing political parties; on the way elections are scheduled, sequenced, and combined; or on the rules for determining the winner within a given election.
With electoral systems one can also focus on the internal voting mechanism that reviews, for instance, in how far the voters' choices are reflected in the outcome. The mechanism can help show that candidates need to focus differently to improve their odds of winning a seat.
Direct comparisons between first-past-the-post and proportional voting
Though there are many different systems, including a large number of combinations of systems, there are two extremes in the range of voting systems that are very different from one another. Viewing the differences between these two can help to attain a quick overview about some of the differences between electoral systems and why the differences have significant political implications. The two systems are:First-past-the-post voting: A single candidate wins the seat of a single district, county or nation, by getting the most votes in a geographical area. Here, "most" means more votes than any other candidate, which can be less than 50 percent of the votes, for example, 20 or 30 percent of the votes. This can be termed a "relative majority" or a ":wikt:plurality|plurality".
Proportional voting: The entire outcome of votes in a municipality or nation translates collectively into the outcome of the seats.
- Where a geographical connection is automatically incorporated in the electoral outcomes in nations with first-past-the-post, there is no certainty about geographical representation in proportional voting. It may play a role with the selection of the candidates, but when geographically inclined voters need to be alert whether candidates are from their own region or area and vote appropriately.
- In first-past-the-post, voters are represented by a single representative, whether they voted for the candidate or someone else. With proportional voting, virtually every voter can point to the representative they voted for.
- If decisions in the elected body are also made by a relative majority of the elected representatives, then the relative majority of the decision-making votes combines with the fact that the representatives won their seats with only a relative majority of their constituents' votes. In effect, this strong dual mechanism diminishes the constituents' importance in the decision; if a seat is obtained with 20 percent of the vote, and a decision is subsequently made with 40 percent of the council members, then the voters' input can be declared as diminished, since about 12 percent of voters have indirectly made the winning decision. If decisions made in proportional voting are won with an absolute majority of the votes by the people who got their seats based on the direct distribution of the constituents' votes, then there is at worst a 50 percent weakening in the representation of voters' opinions, in the sense that a decision represents at least 50 percent of the voters.
- Regions with a first-past-the-post system tend to have a stabilizing factor built in because third-party candidates will have a harder time beating out candidates from Party One and Party Two. Cabinets will not often be based on coalitions and will therefore tend to stay in power for a long time. In general, the two major parties will have no problem absorbing third-party issues as their own, covering any gaps both forgot to cover collectively. Both parties may therefore deliver close to what the voters want. Contrast this with the absence of built-in stability of proportional voting, in which two, sometimes three parties or more, need to cooperate to obtain a workable majority. This shows how one system is more accustomed to having a more vertical power structure whereas the other is more collaborative or horizontal in nature.
- Regions with first-past-the-post have a focus on the center of the constituency. To win a seat, a candidate X must appeal to as many voters as possible, and try to split the remaining votes among rival candidates, so that all the other candidates receive lower support than X. In proportional voting, the focus can follow a party-based policy, and the political message can be quite honest and direct. It is possible that a party obtains seats appealing to voters on the single issue, for example, of non-human animal rights. Candidates and representatives handle information differently in the two extreme systems because the arithmetic of winning seats differs between the two systems.
Mathematical criteria
To compare methods fairly and independently of political ideologies, voting theorists use voting method criteria, which define potentially desirable properties of voting methods mathematically.
Using criteria to compare methods does not make the comparison completely objective. For example, it is relatively easy to devise a criterion that is met by one's preferred voting method, and by very few other methods. Doing this, one can then construct a biased argument for the criterion, instead of arguing directly for the method. There is no ultimate authority on which criteria should be considered.
The following criteria, which apply to single-winner voting methods, are considered to be desirable by many voting theorists:
Result criteria (absolute)
These are criteria that state that, if the set of ballots is a certain way, a certain candidate must or must not win.; Utility criterion
; Majority criterion
; Mutual majority criterion
; Condorcet criterion
; Condorcet loser criterion
Result criteria (relative)
These are criteria that state that, if a certain candidate wins in one circumstance, the same candidate must win in a related circumstance.Ballot-counting criteria
These are criteria which relate to the process of counting votes and determining a winner.Strategy criteria
These are criteria that relate to a voter's incentive to use certain forms of strategy. They could also be considered as relative result criteria; however, unlike the criteria in that section, these criteria are directly relevant to voters; the fact that a method passes these criteria can simplify the process of figuring out one's optimal strategic vote.;Later-no-harm criterion, and later-no-help criterion
;No favorite betrayal
Ballot format
These are issues relating to the expressivity or information content of a valid ballot.;Ballot type
;Equal ranks
;Over 2 ranks
Weakness
Note on terminology: A criterion is said to be "weaker" than another when it is passed by more voting methods. Frequently, this means that the conditions for the criterion to apply are stronger. For instance, the majority criterion is weaker than the multiple majority criterion, because it requires that a single candidate, rather than a group of any size, should win. That is, any method which passes the MMC also passes the MC, but not vice versa; while any required winner under the MC must win under the MMC, but not vice versa.Comparisons
Compliance of selected single-winner methods
The following table shows which of the above criteria are met by several single-winner methods.This table is not comprehensive. For example, Coombs' method, which satisfies many of the criteria, is not included.
Compliance of party-based multi-winner methods
The following table shows which of the above criteria are met by several party-based multiple winner methods.| Proportional in theory | Proportional in practice | Semi-proportional a majority of voters cannot force the result to be one such that they win all seats | Not breakable voting method does not have a potential strategic voting feedback loop | Monotone | Consistency | Participation | Are there tiers of members? | Is local representation required? | Is there voter selection of individual candidates? | Ballot Type | ||
| General ticket | — all seats are filled from one pre-determined list | Single mark for one list | ||||||||||
| Closed party-list | — the ranking of candidates within the party's list determines the order by which the party's seats are filled | Single mark for one list | ||||||||||
| Relatively closed party-list | — a candidate needs to obtain a Hare quota to be guaranteed a seat, otherwise the ranking of candidates within the party's list determines the order by which the party's seats are filled | Single or limited marks for candidates within one list | ||||||||||
| More open party-list | — a candidate needs to obtain a proportion of the votes to be guaranteed a seat, otherwise the ranking of candidates within the party's list determines the order by which the party's seats are filled | Single or limited marks for candidates within one list | ||||||||||
| Most open party-list | — the number of votes every candidate receives determines the order by which the party's seats are filled | Single mark for one candidate within one list | ||||||||||
| Party-list with panachage | — the number of votes every candidate receives determines the order by which the party's seats are filled | Limited marks for candidates within all lists | ||||||||||
| Unmodified Mixed-member proportional | — constituency tier and proportional tier | — single-member constituencies | — constituency candidates are selected by a single-winner method; selection of proportional tier members may be done by any of the party-list methods mentioned above | Single mark or ranking for one constituency candidate; proportional tier marks depend on the exact method used for selection | ||||||||
| Best-loser Mixed-member proportional | — constituency tier and proportional tier | — single-member constituencies | — constituency candidates are selected by a single-winner method; proportional tier members are selected by a party-list method | Single mark or ranking for one constituency candidate; proportional tier determined by the constituency tier results | ||||||||
| Parallel voting | — constituency tier and proportional tier members are selected independently of each other | — constituency tier and proportional tier | — single-member constituencies | — constituency candidates are selected by a single-winner method; proportional tier members are selected by a party-list method | Single mark or ranking for one constituency candidate; proportional tier marks depend on the exact method used for selection | |||||||
| Scorporo | — constituency tier and proportional tier | — single-member constituencies | — constituency candidates are selected by a single-winner method; proportional tier members are selected by a party-list method | Single mark or ranking for one constituency candidate; proportional tier marks depend on the exact method used for selection | ||||||||
| Majority bonus system | — proportional tier and bonus tier | Proportional tier marks depend on the exact method used for selection; bonus tier determined by the proportional tier results | ||||||||||
| Majority jackpot system | — the party gaining the jackpot gains an advantage over all others; the jackpot turns into a disadvantage for the most-voted-for party if it gained a greater share of seats than the jackpot | — proportional tier and jackpot tier | Proportional tier marks depend on the exact method used for selection; jackpot tier determined by the proportional tier results | |||||||||
| Dual-member proportional | — dual-member constituencies | — the candidate with the most votes is guaranteed a seat, and the other is selected from among the best losers | Single mark for one candidate or pair of candidates | |||||||||
| Rural–urban proportional representation | — urban tier, rural constituency tier and rural proportional tier | — urban constituencies and single-member rural constituencies | — rural constituency candidates are selected by STV; rural constituency candidates are selected by a single-winner method; rural proportional tier members may be selected by a party-list method or from among the best losers in the rural constituencies | Ranking for urban constituency candidates; single mark or ranking for one rural constituency candidate; rural proportional tier marks depend on the exact method used for selection |
Compliance of non-majoritarian party-agnostic multi-winner methods
The following table shows which of the above criteria are met by several multiple winner methods.| Proportional | Monotone | Consistency | No Favorite Betrayal | Semihonest | With Single Winner | Ballot Type | |||
| Approval or Range | Approvals or scores | ||||||||
| Approval or Range | Approvals or scores | ||||||||
| Approval or Range | Approvals or scores | ||||||||
| Approval or Range | Approvals or scores | ||||||||
| Sequential Proportional Approval | Approval | Approvals | |||||||
| Re-weighted Range | Range | Scores | |||||||
| Proportional Approval | Approval | Approvals | |||||||
| Approval or Range | Approvals or scores | ||||||||
| Single Transferable Vote | Instant Runoff | Rankings | |||||||
| CPO-STV | A Condorcet method | Rankings | |||||||
| Schulze STV | Schulze | Rankings | |||||||
| Approval | Approvals | ||||||||
| Single non-transferable vote | Plurality | Single mark | |||||||
| Limited vote | Plurality | Limited marks | |||||||
| Cumulative voting | Plurality | Multiple marks | |||||||
| Approval | Approvals | ||||||||
| Sortition, Arbitrary Winner | Sortition, arbitrary winner | ||||||||
| Single Random Ballot | Random Ballot | Limited marks | |||||||
| Multiple Random Ballots | Approaches | Random Ballot | Limited rankings |
Compliance of majoritarian party-agnostic multi-winner methods
The following table shows which of the above criteria are met by several multiple winner methods.| Monotone | Consistency | Participation | Cloneproof | No favorite | Semihonest | Smith set | Condorcet | Condorcet | With single | Ballot | |
| data-sort-value="2" | Approval | Approvals | |||||||||
| Multiple Winner Range | Range | Scores | |||||||||
| Multiple Winner Schulze | Schulze | Rankings | |||||||||
| At Large | Plurality | Limited marks |
Experimental criteria
It is possible to simulate large numbers of virtual elections on a computer and see how various voting methods compare in practical terms. Since such investigations are more difficult than simply proving that a given method does or does not satisfy a given mathematical criterion, results are not available for all methods. Also, these results are sensitive to the parameters of the model used to generate virtual elections, which can be biased either deliberately or accidentally.One desirable feature that can be explored in this way is maximum voter satisfaction, called in this context minimum Bayesian regret. Such simulations are sensitive to their assumptions, particularly with regard to voter strategy, but by varying the assumptions they can give repeatable measures that bracket the best and worst cases for a voting method. To date, the only such simulation to compare a wide variety of voting methods was run by a range-voting advocate and was not published in a peer-reviewed journal. It found that Range voting consistently scored as either the best method or among the best across the various conditions studied.
Another aspect which can be compared through such Monte Carlo simulations is strategic vulnerability. According to Gibbard's theorem, no deterministic voting method can be immune to strategic manipulation in all cases, but certainly some methods will have this problem more often than others. M. Balinski and R. Laraki, the inventors of the majority judgment method, performed such an investigation using a set of simulated elections based on the results from a poll of the 2007 French presidential election which they had carried out using rated ballots. Comparing range voting, Borda count, plurality voting, approval voting with two different absolute approval thresholds, Condorcet voting, and majority judgment, they found that range voting had the highest strategic vulnerability, while their own method majority judgment had the lowest.
Balinski and Laraki also used the same information to investigate how likely it was that each of those methods, as well as runoff voting, would elect a centrist. Opinions differ on whether this is desirable or not. Some argue that methods which favor centrists are better because they are more stable; others argue that electing ideologically purer candidates gives voters more choice and a better chance to retrospectively judge the relative merits of those ideologies; while Balinski and Laraki argue that both centrist and extremist candidates should have a chance to win, to prevent forcing candidates into taking either position. According to their model, plurality, runoff voting, and approval voting with a higher approval threshold tended to elect extremists ; majority judgement elected both centrists and extremists ; and range, Borda, and approval voting with a lower approval threshold elected centrists. However, their model did not take into account voters' strategic reactions to the method used, such as "lesser of two evils" voting under plurality.
Simulated elections in a two-dimensional issue space can also be graphed to visually compare election methods; this illustrates issues like nonmonotonicity, clone-independence, and tendency to elect centrists vs extremists.
"Soft" criteria
In addition to the above criteria, voting methods are judged using criteria that are not mathematically precise but are still important, such as simplicity, speed of vote-counting, the potential for fraud or disputed results, the opportunity for tactical voting or strategic nomination, and, for multiple-winner methods, the degree of proportionality produced.The New Zealand Royal Commission on the Electoral System listed ten criteria for their evaluation of possible new electoral methods for New Zealand. These included fairness between political parties, effective representation of minority or special interest groups, political integration, effective voter participation and legitimacy.