Abstract
What is the proper interpretation of the majority rule when the number of proposals or candidates is greater than two? This problem is first discussed in Aristotle’s Politics. The chapter provides historically informed description of voting rules. When there are more than two alternatives, the most important criteria of reasonability or fairness are the Condorcet criterion, the Borda criterion, and the plurality criterion. Arguably, all the real-life methods of choosing a single alternative or candidate may be seen as realizations or as approximations of, or compromises between, these three competing criteria. The social choice criteria are applied to the institutions of direct democracy. A fourth criterion for democratic choices is proportionality. Unlike the other criteria, proportionality is linked, not only to the problem of multiple alternatives, but also to the problem of the two-stage process of representation. I refute some traditional criticisms of proportionality, and try to show why proportionality is compatible with the use of the Condorcet criterion and hence a majoritarian interpretation of democracy. Ultimately, any attempt to apply the criteria in a mechanical way may produce what I call the meta-paradox of social choice. The important message of social choice results is that there are unavoidable trade-offs: we cannot have all the good things simultaneously. What we need is a substantial political theory which tells us how to navigate through the trade-offs.
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Notes
- 1.
The Superior Electoral Tribunal of Brazil had to face a similar problem of interpretation in 1951. According to the 1946 Constitution and the 1950 electoral code, the President of the Republic was to be elected according to “the majority principle”. The Tribunal decided that a plurality would be sufficient.
- 2.
For example, of the 43 voting rules examined by Warren Smith (2006), only eight have been used—or even seriously considered—in actual decision-making outside laboratories.
- 3.
- 4.
- 5.
The democratic compromise, unlike the classical Bucklin rule, asks voters to rank all the candidates.
- 6.
Niou (1987) remarks that the Nanson rule is often misstated in the social choice literature.
- 7.
Cf. Bertold Brecht’s famous poem Die Lösung: “Wäre es da/Nicht doch einfacher, die Regierung/Löste das Volk auf und/Wählte ein Anderes?”
- 8.
In the small canton of Appenzell, women got their voting rights as late as 1989. The struggles for general suffrage in the late nineteenth and the early twentieth century also provide examples of the problem. The representatives elected on the basis of a limited suffrage often resisted attempts to make electoral systems more democratic and the democrats had to resort to extra-parliamentary and sometimes extra-constitutional activity. In Belgium, the introduction of general suffrage was preceded by a long and sometimes violent struggle led by the Socialists (from 1886 to 1913). After the First World War the bourgeois and the Socialist parties reached a general agreement on the need for an electoral reform. The constitution demanded new elections before a constitutional change could be accepted. Because the Socialists and the Liberals refused to accept any further elections to be held according to the old unequal electoral system, the system was finally (1919) changed in an unconstitutional way.
- 9.
Greece is another striking example of electoral manipulation. Between 1920 and 1980, almost all elections were conducted under different rules. From 1920 to 1936, there were five major changes (from the runoff to a proportional system and from a proportional system back to the runoff etc.). After the War, there was one experiment with the plurality (demanded by the US Ambassador) and several experiments with different versions of proportional representation. According to one commentator “In the post-war period manipulation of the electoral system has been one of the principal means by which the Right has sought to contain the Left and to perpetuate its hold on power” (Clogg, 1984, 190). This practice has continued. In 1989 the Leftist PASOK government introduced a more proportional electoral law in order to minimize the expected victory of the Right. In 1990, the Rightist government curtailed the proportionality again. In the Polish 2001 elections, the opponents of the Social Democrats altered the electoral law in order to prevent a Social Democratic majority government, by replacing the d’Hondt system by a modified Sainte-Laguë and by increasing the district magnitude. Both changes favoured middle-sized parties. The emergence of a Social Democratic majority was prevented, but the main architects of the new system did not themselves profit from the change (Millard, 2003, 70–71).
- 10.
“In elections the vote of each member has about the same weight” (Dahl & Lindblom, 1953, 41).
- 11.
“Elections (…) must decide, in some basic way, the outcome of the competition for power and policies”. (Harry Eckstein, cited after Barry, 1970, 54).
- 12.
According to Bellamy (1999, 132) “we need a voting system for both selecting representatives and making policies in the legislature that builds in compromise to majoritarian decision-making”. Mackie (2006) uses the term centrality: “A democratic voting rule should select the central tendency among individuals’ rankings” (p. 15).
- 13.
Outside the United States, the tendency in “majoritarian” systems has been clear. In the French parliamentary (runoff) elections in 1877, 98 % of the seats were filled in the first ballot by an absolute majority of the votes, and the average number of candidates was two; in 1978 the respective numbers were 13 % and 9. In the post-war Britain, nine MPs out of ten were elected by an absolute majority; now only a half of them, and in some elections only a third.
- 14.
See Goodin and List (2006). The authors actually argue that the plurality rule satisfies May’s strong monotonicity (or positive responsiveness) condition. The problem with this claim is that, unlike May, Goodin and List seem to discuss vote aggregation rather than preference aggregation; otherwise their proof cannot be valid. In the context of two alternatives, the difference between these approaches is without consequence; if there are only two alternatives, voters are always able to express their full preference orderings. With more than two options, however, the plurality rule is not strongly monotonic if the arguments of the choice function are voters’ preferences rather than votes cast. This is shown by the following fact: if two or more alternatives tie, a change in the lower preferences of the voters is not sufficient for breaking the tie if, as with the plurality rule, they are able to express only their first preferences.
- 15.
In a plurality election with k candidates and N voters, the winner may be the worst choice for all but (N/k) + 1 voters. Thus, in a three-candidate election, he or she may be the worst choice for almost two-thirds of the voters.
- 16.
- 17.
The first recorded disputes on the respective merits of the majority-principle and the Borda principle appeared in the sixteenth and seventeenth centuries when a Borda-type positional system was used in Belgium. The interpretation of electoral results caused some disagreement. Pope Gregory XV (Pope 1621–1623) decided that when “the number of votes” and “the number of voters” pointed to different directions, the latter was decisive (Moulin, 1958, 517).
- 18.
Chakravarty and Hojman (1999) argue that actually there was no Condorcet winner in the 1970 Chilean elections. However, the opinion measurements cited by Valenzuela (1978, 42) indicate that Allende was an absolute loser in 1970: 56.6 % of the respondents rejected his candidacy, while a little more than 40 % opposed the candidacies of Tomic and Alessandri. See also Colomer (2001, 115); on the same problem in the other Latin American elections, see Colomer (2007).
- 19.
According to Key (1950) 36 % of the runoff contests in the (US) Southern primaries went to the second-place candidate. Glaser (2006) finds that 28 % of the 117 Southern Congressional primaries that went to a runoff between 1980 and 2002 were won by the candidate who placed second in the first contest. In those cases the first-ballot plurality winner was not a Condorcet winner.
- 20.
Of course, this result does not show that Chirac was not a Condorcet-winner; he might have defeated Jospin too, although not with such a margin. Abramson (2007) has provided some evidence that in the 2007 French elections, the Condorcet-winner was not the runoff-winner Nicolas Sarkozy but François Bayrou who came in as the third in the first round.
- 21.
The empirical work of Felsenthal and Machover (1995) is compatible with these results. Colomer (2007) estimates that in the Latin American presidential elections the Condorcet-winning candidates have won the presidency in about two-thirds of plurality elections and three-fourths of runoff-elections. The effective numbers of candidates in these elections have been 3–5; hence Colomer’s estimations are roughly compatible with Merrill’s simulations. Fishburn and Gehrlein (1982) have shown that (i) the top-two runoff-rule elects Condorcet—winners more often than the weaker runoff-rules, and that (ii) the standard Borda rule is, in Condorcetian terms, better than any of its modifications.
- 22.
Narrow pluralities and/or close results have often motivated the change to runoff-elections. Examples of such changes are the adoption of the presidential election-rules in Chile (the 1989 constitution), Dominican Republic (1994) and Uruguay (1997) as well as in the Democratic primary elections in Arkansas (1937) and New York (1972). Shugart and Taagepera (1994) and O’Neill (2007) have argued that while a runoff makes it more likely that a Condorcet-winner is chosen, it introduces unnecessary costs when the plurality winner also happens to be the Condorcet-winner. If the winner’s share of votes in the first ballot is close to 50 % and if the margin between her and the runner-up candidate is wide, it is probable that she would also win the runoff. This justifies the use of qualified pluralities (see Sect. 3.1.3). Another possible (utilitarian) justification for qualified plurality runoffs—not discussed by O’Neill—is that a candidate with relatively wide (say, 45 %) first-preference support might be a better choice than a Condorcet-winner with a wider but lukewarm low-preference support.
- 23.
In an empirical study on the phenomenon Richard S. Katz (2001, 144–145) concludes that the probability of “spurious” majorities in plurality elections is 5–10 %. According to Colomer (2001, 102–103) it has happened ten times in the nation-wide elections in the USA, three times in Canada, four times in New Zealand and six times in the UK. In the US-American and Canadian state/provincial elections it has been a more common phenomenon. Katz (2001, 144–145) finds as many as 41 cases in the elections of the lower houses in the US states between 1968 and 1994, and 11 cases in the Canadian provincial elections since 1949. Siaroff (2003) shows how the phenomenon has also been relatively common in the Australian AV-elections.
- 24.
In a two-party contest with single-member constituencies of equal size, a party may gain a parliamentary majority with 25 % of the votes. With SNTV in two-member constituencies, the theoretical minimum is 33.3 %. The effectiveness of gerrymandering decreases when the number of representatives elected from constituencies increases: if M is the number of seats in a constituency, the minimum proportion of votes needed to secure a majority in a majority of constituencies of equal size is (M/M + 1)/2. When M increases, this approaches to one half of the votes.
- 25.
The limited version of AV which allows only the expression of first and second preferences (see Lusch, 1907) suffers from the same problem. However, because it eliminates candidates one-by-one, it works like the supplementary vote in the Example 3.5 but not in Example 3.4. Of course, the notion of “wasted vote” is a tricky one. Ultimately, I think, the notion has to be based on a moral argument. A supporter of Al Gore in Florida 2000 might have criticized someone who was going to vote for Ralph Nader: “If everyone like you will act in that way, George W. Bush wins, and your votes are just wasted”. If, however, the supporter of Nader would have replied: “Bush or Gore, I don’t care; I just want to express my true opinion”, there is no further reason to call her vote “wasted”.
- 26.
Consider a case which blatantly violates Duverger’s Law. Papua-New Guinea applies the plurality rule in single-member constituencies. In the elections of 1992 there were 1654 candidates competing in 109 constituencies; the average number of candidates per constituency was 15.2. The result was that in eight constituencies, the winners got less than 10 % of the votes of their electorates; in 40 they got 10–20 %, and only in 28 out of 109 did the winners receive more than 30 % of the votes (Reilly, 1997b). This is not a surprising result in a country with about 1000 different linguistic and ethnic groups. How would the standard justifications of the plurality rule work in these conditions? Certainly, we cannot say that it at least approximates to the beneficial properties of majority rule.
- 27.
- 28.
Sager’s (1998) account is earlier but less detailed; here I follow Hylland’s narrative.
- 29.
Thus the common references to “cardinalization” of preferences as a solution to the Arrovian problem are mistaken; the issue is interpersonal comparability, not the applicability of a particular measure function. An example of this mistake is Hoevenkamp (1990) in which the whole Arrowian problem is reduced to the problem of “cardinalization”. Sen (1982, Part III) makes the issue clear. For example, the Rawlsian difference principle requires interpersonal comparisons—otherwise we could not identify the least advantaged group—but not cardinal comparisons. Boadway and Bruce (1991, ch. 5) give an excellent summary of various informational requirements in the context of welfare economics.
- 30.
- 31.
A reminder: May’s strong monotonicity (or positive responsiveness) condition requires that if a voter changes her vote to favour an otherwise winning option it remains a winner, and if she changes her vote to favour an otherwise tied option it becomes a winning one—unless there are simultaneous changes to the opposite direction. Nurmi (1987, 77–78) shows that the Borda rule and the amendment rule—unlike most rules in general use—satisfy this requirement (contra Mackie, 2003). As Nurmi says (p. 69) it is “something of a luxury”; however, it guarantees that all information on voters’ preferences is utilized in decision-making and thereby maximizes the power of an individual voter.
- 32.
- 33.
When making this proposal Dummett, in effect, abandons his earlier “insufficient reason”-argument.
- 34.
Indeed, Sugden (1981, 143) admits that his intensity-based argument does not pick the Borda rule as the uniquely best “neo-utilitarian” rule.
- 35.
- 36.
There are infinitely many positional voting rules (Feldman, 1980); thus, the result showing the unique status of the Borda rule among them is highly significant. Notice, however, that Saari’s uniqueness result is related to ordinal rules only. Utilitarian voting rules which go beyond ordinality, like Heckscher’s “immanent method” (a.k.a. range voting) also satisfy Saari’s two neutrality requirements.
- 37.
At least in planning and in ethical contexts where individual rankings may represent different decision criteria rather than individual preferences, a cyclical result cannot be automatically treated as a tie, that is, as indifference between the alternatives involved in a cycle. Rather, it may be interpreted as incommensurability between different criteria of goodness.
- 38.
See, however, Fraenkel and Grofman (2014) on the Dowdall system used in Nauru and the limited version of Borda used in Slovenia. Their study confirms the general picture: in politically important elections Borda-like systems actually invite agenda manipulation and strategic voting.
- 39.
Something similar happens when the cumulative vote is used. Cumulative voting allows a voter to distribute a fixed number of votes among the candidates according to her preferences. Thus, it is an example of a point-voting system, and could be conceived as one possible method for making intensity comparisons. Unlike the Bentham-Heckscher rule, however, it is not path-independent. And, as Felsenthal (1990) has shown, when voters use rational strategies, cumulative vote is reduced to the simple plurality. A vote-dividing strategy never dominates and is often dominated by the strategy in which voters vote for their favourite candidate only. It is reasonable to expect that all rules which really give voters an opportunity to express preference intensities suffer of the same problem (see also Jones, 1988, 14–15; Saward, 1998, 77–78).
- 40.
Tideman (2006, 238) argues that the Borda rule and Hillinger’s “utilitarian” voting should be used only when people act as disinterested judges; in other words, only when they do not try to maximize their own utilities. Another work which takes the measurement analogy as granted and, consequently, treats voters as disinterested judges is that by Balinski and Laraki (2010).
- 41.
This sentence is a surprising slip in Budge’s admirable and otherwise impeccably democratic book.
- 42.
Fishkin’s “deliberative poll” (Fishkin, 1991) operates with a randomly selected demos. However, although he recommends its use as an aid in democratic decision-making, he does not propose that it should replace general elections.
- 43.
Fishkin (1991, 83) quotes a study on opinion measurements: “Most respondents feel obliged to have an opinion, in effect, to help the interviewer out. (…) In effect, opinions are invented on the spot.”
- 44.
For an opposite argument, see Ankersmit (1996), 408: “Arrow argues here that no rules that are both workable and ethically acceptable can be developed for translating the wishes of the voters into actual policy. In fact, this theorem is fatal for all conceptions of direct democracy (…).” (emphasis EL).
- 45.
- 46.
In Denmark, there were two referenda on the European integration: one on the Maastricht Treaty (1992) and another on its amended version, the Edinburgh Agreement (1993). Only 49.3 % of the Danish voters accepted the original treaty, while 56.7 % accepted the amended version. Justesen (2007) estimates that in a plurality contest between three options (the original treaty, the amended version and no treaty), the amended version would have been a plurality loser, preferred to the other alternatives only by 12–29 % of the electorate. Nevertheless, it was a Condorcet (and Borda) winner.
- 47.
- 48.
The Swiss Constitution, Art 139 b: “Ils peuvent approuver les deux projects à la fois. Ils peuvent indiquer, en réponse à la question subsidiaire, le projet auquel ils donnent la preference au cas où les deux seraint acceptés.”
- 49.
Some of the US methods were discussed by Herbert Tingsten in his early study on the referendum institution. His work also contains perceptive observations about the strategic properties of the rules (Tingsten, 1923, 178–182).
- 50.
The Constitution of California Art 2. Sec 10(6) “If provisions of 2 or more measures approved at the same election conflict, those of the measure receiving the highest affirmative vote shall prevail.” Cf. the Constitution of Michigan, Art II Sec 9.
- 51.
The Constitution of Maine, Art. IV Sec. 18.2. “When there are competing bills and neither receives a majority of the votes given for or against both, the one receiving the most votes shall at the next statewide election to be held not less than 60 days after the first vote thereon be submitted by itself if it receives more than 1/3 of the votes given for and against both.”
- 52.
The Constitution of Washington, Art. II Sec. 1. “When conflicting measures are submitted to the people the ballots shall be so printed that voter can express separately by making one cross (X) for each two preferences, first, as between either measure and neither, and secondly, as between one and the other. If the majority of those voting on the first issue is for neither, both fail (…). If a majority voting on the first issue is for either, then the measure receiving a majority of the votes on the second issue shall be law.”
- 53.
Further information about the use of counter-initiatives in the USA can be found in Bowler et al. (1998), pp. 4, 99, 109–129.
- 54.
Benoit (2000) argues that the seat distribution rule tends to have a significant effect when the number of seat per constituency is between 5 and 15.
- 55.
- 56.
In many languages, there is an alternative verb for political representation: vertreten in German, företräda in Swedish, edustaa in Finnish. For those who think that etymology may be philosophically informative, these expressions should give some food for thought. Unlike “representation”, these verbs cannot be related to the mysterious “virtual presence of those who are physically absent”. Rather, the connotation is that the representative walks or stands before those who are represented and who, therefore, must be physically present. My intention is not, however, to build a new theory of representation on this observation but only to illustrate the limits of “linguistic” arguments based on the idiosyncrasies of particular languages.
- 57.
For example, both Count de Mirabeau and John Adams spoke about the legislature as a “portrait” of the nation—but neither of them was referring to any scheme of proportional representation in the modern sense of the word.
- 58.
Both Jones (1983) and Brighouse and Fleurbaey (2008) contrast ‘fair distribution’ or ‘the principle of proportionality’ to the majority principle and see the former as an alternative to the latter. However, they fail to pay sufficient attention to the necessary presuppositions of their alternative schemes. For example, Brighouse and Fleurbayeu (ibid., 1–2) argue that “power should be distributed in proportion to people’s stakes in the decision under consideration. Stakes, here, measure how people’s interests are affected by the options available in the decision (…)”. They admit that interests cannot be treated in a neutral way, but “should be evaluated in connection with a conception of social justice”. In order to distribute the power in an appropriate way, we should, then, first find out who are affected, what are their interests, and what would be a just way to treat those interests. Similarly, Jones’s scheme presupposes that we can count the number of ‘issues’, identify the winners and losers in each issue, and assess the relative importance of wins and losses to each group.
- 59.
As we saw, attempts to constrain and modify the seat allocation by bonus seats, thresholds, and mixed rules may violate responsiveness conditions. Due to such additional devices, parties may lose seats by increasing their share of the votes, and win some seats by losing votes. Anonymity is violated by all systems based on separate constituencies; the compound majority paradoxes discussed in Sect. 2.2.3 provide some simple examples. Neutrality, however, is respected by most electoral systems.
- 60.
McGann (2006, 24) argues that independence is not a quality that we should require of seat allocation rules. However, his notion of “binary independence” is defined in terms of rankings, not in terms of seat allocation. Suppose that parties a and b have an equal number of votes and seats. Then, a third party, c, gains some votes and seats at the expense of party b. This change would necessarily affect the relative positions of a and b in the ranking of parties, violating McGann’s version of independence. In this sense, “independence” is certainly not a desirable property. In another sense, however, independence is violated only if the vote distribution between b and c affects a’s absolute share of seats. This is likely to happen in PR-systems which favour large parties. This latter version of “independence” is intuitively more plausible.
- 61.
Gerrymandering is the most drastic way of violating van der Hout’s and McGann’s anonymity condition (i). It is also an important aspect of the Locke problem (Sect. 3.1.6). While districting is usually an important issue in the SMD-systems, it is much less salient in PR-systems.
- 62.
- 63.
The most important exception of this is the Borda count which registers all preferences, and is therefore strongly monotonic.
- 64.
For the notion of an Arrowian social welfare ordering, see (Arrow 1951/1963). The mistaken claim that the purpose of PR election is to produce a social ordering appears, for example, in Riker (1984a, 106) and in Bonner (1986, 92). There are, however, individual cases in which the ordering of the parties in a parliament is relevant for the final choice. Consider Art. 37. Sects. 2 and 3 of the Constitution of Greece: “…the President of the Republic shall give the leader of the party with a relative majority an exploratory mandate in order to ascertain the possibility of forming a Government (…). If this possibility cannot be ascertained, the President of the Republic shall give the exploratory mandate to the leader of the second largest party in the Parliament, and if this proves to be unsuccessful, to the leader of the third largest party in Parliament.”
- 65.
Bonner (1986, 93) remarks, “If it were practicable for voters to rank the names on party lists, or to delete candidates they disliked, the outcome could be more responsive to the detailed preferences but sophistication, manipulation, and the irrelevance aspect would be reintroduced.”
- 66.
- 67.
In 1982 the withdrawal of the FDP caused the fall of the third Schmidt cabinet and the establishment of the first Kohl cabinet. This is probably the most dramatic example of the disproportionate influence of the FDP in German politics.
- 68.
Actually, the matter is quite tricky. As Manfred Holler has argued, my unwillingness to do something does not mean that I do not have the power to do it. However, if I can only acquire power to do things I do not want to do, I have no rational motive to acquire power. In such a situation, power has no value for me. Hence, the notion of power cannot be used to explain or predict my behaviour in such situations. This problem does not make power indices useless. They may provide some guidance for evaluating institutionally fixed allocations of power. The allocation of power between different countries in the institutions of the European Union is a good example of such a context. The expression “the value of power” is taken from Holler.
- 69.
Such schemes are particularly relevant in federal contexts, e.g. in the EU. However, because the actual influence of decision makers is dependent on coalitions (and, ultimately, on decision makers interests) no scheme of power-sharing can guarantee a proportional distribution of influence over outcomes.
- 70.
In modern times, proportional power-sharing has often been incorporated into agreements made after civil wars. Examples of this are the Colombian pact between the Blancos and the Colorados, the Lebanese agreement in 1943, the 1960 constitution of Cyprus, the Good Friday accord in the Northern Ireland, and the present constitution of Bosnia-Herzegovina. They tried to guarantee peace by distributing power between various groups in a pre-determined way. The problem with these non-anonymous and non-neutral schemes is that they tend to cement the prevailing interests and power-relations.
- 71.
The thesis is well formulated—although not necessarily endorsed—by Blais (1991, 247): “Real political decisions are made through majority rules and it is ‘natural’ to apply the same logic in the selection of decision-makers.” For positions similar to that of Ganghoff, see McGann (2004, 2006) and Riley (1988).
- 72.
The connection between the median voter position and the Condorcet winning position is simple: if the voters can be ordered on one single axis (usually, Left-Right) according to their opinions, there are equal numbers of voters—less than a half—on the Left and on the Right side of the median position. The median voter is pivotal; the alternative supported by him/her is the Condorcet-winning-alternative.
- 73.
This conclusion is, of course, incompatible with the popular argument that the plurality systems usually provide a “clear choice” for voters. It is also incompatible with the Hobbesian conception of power mentioned above. To quote Lijphart again: “Parties are not pure power-maximizers. They want to participate in cabinets not just in order to hold a share of governmental power but also to collaborate with other like-minded parties to advance particular policies” (Lijphart, 1984, 58).
- 74.
Of 25 Western democracies, only in nine has there been “a clear connection” between electoral results and government changes. Among these nine, two countries use the plurality rule, four use list-PR systems, and three use others systems (Ware, 1989, 15).
- 75.
According to Laver and Scofield (1990, 113), of the all European coalition governments formed in 1945–1987, mainly in countries using a PR system, over 80 % contained or were supported by parties that occupied a median position on the right–left dimension. This gives further support to the hypotheses that the voters’ preferences were single-peaked and that the winning coalitions were often Condorcet-winners.
- 76.
Jack H. Nagel’s study (2012) on the democratic performance of New Zealand before and after the move from a plurality system to a (mixed) PR-system gives further support for the thesis that proportional representation “is important not just to serve representational goals, but also to achieve majoritarian goals: a government supported by a majority of voters, a governing party that represents the median voter, and specific policies acceptable to majorities that may—and should—differ from issue to issue” (Nagel, 2012, 10).
- 77.
Budge and McDonald (2009) have qualified their median mandate-thesis. When a plurality party is large and has a commanding lead over its rivals—say a 46 % vote share and a 20 % lead—it can be said to represent the majority will even when a “careful analyst” would judge a smaller party as the median party. Their limited endorsement of the plurality mandate in cases like this is based on epistemic considerations. If only a small fraction of voters do not think in uni-dimensional terms, the plurality winner may actually be the Condorcet-winner in spite of the estimation made by “the careful analyst”: For a similar probabilistic argument for qualified runoff—rules in single-office elections, see Shugart and Taagepera (1994) and O’Neill (2007). Cf. note 21 above.
- 78.
Consider, for example, the comparisons made, respectively, by Warren D. Smith (2006) and by Dan S. Felsenthal (2010). Smith compares 43 (!) voting rules, using 15 formal criteria plus some informal ones, while Felsenthal compares 17 rules using 14 weighted criteria. In Smith’s comparisons, the approval and range voting emerge as the best, while all the Condorcet- consistent rules fare rather badly. By contrast, in Felsenthal’s comparisons the approval and range voting are the worst systems, while two Condorcet-consistent rules (Kemeny’s and Copeland’s) emerge as the winners!
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Lagerspetz, E. (2016). On Voting. In: Social Choice and Democratic Values. Studies in Choice and Welfare. Springer, Cham. https://doi.org/10.1007/978-3-319-23261-4_3
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