At legislative elections, parties can experience different biases in the translation of votes to seats. Grofman, Koetzle, and Brunell published a taxonomy of these biases (Malapportionment, turnout differences, and the geographic distribution of party vote shares). Often, and especially by advocates of proportional representation, the biases are measured and discussed in terms of disproportionality between seats and votes.

Proportionality isn't the only goal out there. Powell's book Elections as instruments of democracy: Majoritarian and proportional visions, following Lijphart, likewise describes the competing electoral systems that uphold majoritarian traditions, in which a small majority is entitled to most powers. Westminster-style legislatures like the House of Representatives and Lok Sabha are on this side, and they have been the target of attempted electoral reform forever. The reform push seems kind of one-sided; advocates of proportionality are not few, but I haven't found many advocates of majoritarianism.

Looking for theoretical justifications, all I found were descriptive statements like Mao's "the minority is subordinate to the majority" and Duverger's Law. Defenses of the majoritarian systems already out there can be confounded by either system justification (in which the status quo tends to appear essentially good and worthy) or by authorial selection bias (in which well-educated writers favor the economic arrangements that afford them relative privilege).

Are there theoretical rationales supporting majoritarian legislative election results?

  • Since you seem to look for a very specific answer, can you clarify what you mean by majoritarian? There are competing definitions (see my answer).
    – Fizz
    Sep 29 '18 at 0:50
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    @Fizz Majoritarian legislative election results are when a winning party gets a greater share of seats than they got votes. This is as opposed to proportional results, in which each party's seat share matches their vote share. Sep 29 '18 at 0:57
  • I see; the issue is that almost all the literature debates election systems, not election outcomes. To define majoritarian in your terms is to mostly concede to the proportional point-of-view. But I guess your question is still answerable.
    – Fizz
    Sep 29 '18 at 1:02
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    I don't know if you get an automatic notification for this, but I've substantially edited my answer since your focus is different than what I first thought.
    – Fizz
    Sep 29 '18 at 5:31
  • I've suggested an edit to clarify the meaning of "majoritarian". Please check and of course feel free to roll back. BTW, I'm no expert on the topic, but I'd think you'll find some ideas in Robert Dahl's work on "polyarchy".
    – henning
    Sep 29 '18 at 8:29

The IDEA book, has among the advantages of first past the post one that might answer your question (on majority-biased outcomes):

[b.] It gives rise to single-party governments. The ‘seat bonuses’ for the largest party common under FPTP (e.g. where one party wins 45 per cent of the national vote but 55 per cent of the seats) mean that coalition governments are the exception rather than the rule. This state of affairs is praised for providing cabinets which are not shackled by the restraints of having to bargain with a minority coalition partner.

Likewise John Curtice (2015) says:

According to its advocates, the single-member plurality electoral system enables the electorate to choose directly between alternative governments by ensuring that whichever party comes first in votes secures an overall majority in seats, even though it may have won much less than half the vote.

And he actually cites this argument to Powell's book. But Curtice goes on to criticize it as not being delivered in practice as often as its (unnamed) proponents claim.

And David Cameron has phrased roughly the same argument as:

Throughout history, [FPTP] has risen to the demands of the time, often with a brutal decisiveness.

That’s what happened when it brought in the Thatcher government in 1979.

The British people recognised it was time for change – and the electoral system didn’t let them down.

He doesn't seem wrong with that example, as the Conservative bonus was approximately 9.5% in that election (53.4% of seats vs 43.9% of votes). But the example Cameron gave is about average for the UK; according to Norris (1997)

In the postwar period, for example, British governments have received, on the average, 45 percent of the popular vote but 54 percent of seats.

And Norris also elaborates on the single-party government issue:

The classic argument for majoritarian systems is that they tend to produce stable and responsible single-party governments, so that the electoral outcome is decisive. In contrast, unless one party wins a majority of votes, PR is closely associated with coalition cabinets. A survey of twenty countries found that single-party governments were formed after 60 percent of majoritarian elections, but only 10 percent of PR elections (Blais and Carty 1987). If we compare the parliamentary democracies in this analysis 56.3 percent of elections under majoritarian systems produced single-party governments, compared with 36.4 percent of elections under mixed systems, and 34.8 percent of PR elections. In countries with PR and fragmented party systems, like Italy, the Netherlands and Switzerland, all governments tend to be coalitions. But majoritarian electoral systems can also result in coalition governments, such as in Britain between the wars. Moreover PR systems may also have single-party governments, such as long periods of dominance by the Austrian Socialists, the Norwegian Labour party, and the Swedish Social Democrats. The pattern of government formation is therefore far more complex than any simple linear relationship might lead us to expect (Laver and Shepsle 1995), although as expected there is a significant relationship between the production of single party governments and majoritarian electoral systems.

And Blais appears to have been a major researcher of this question (although hardly the first one). A 1991 paper of his notes:

There can be no doubt that one-party government is more likely to occur under plurality than under proportionality rule, as Rae’s (1969: 99) data indicate: "In 75 legislatures elected under P.R. formulae, the mean minimal majority was 1.96 parties. Typically, the support of the two largest parties was required for the formation of the majority. In 45 legislatures elected under majority and plurality formulae, the mean minimal majority was only 1.15 parties, suggesting that one-party majorities were more common."

Blais and Carty (1988) indicate that 72% of single-member district plurality elections produce a one-party legislative majority, compared to 10% of PR elections. Blais and Carty (1987) also show that, everything else being equal, the probability of a one-party majority government is 40 percentage points higher in a plurality than in a PR election. These findings can be interpreted in two different ways. On the one hand, the plurality rule (in single-member constituencies) generates majorities most of the time and much more frequently than PR. On the other hand, it fails to achieve its basic stated objective three times in ten and it is not even the most efficient procedure in that regard: as Blais and Carty (1988) point out, multi-member district majority elections have produced one-party majority governments nine times in ten. In short, the plurality rule greatly increases the likelihood of a one-party government but is not entirely successful on that score.

Although not as explicit, the following passage from a Fraser Institute paper advocating FPTP, is probably arguing the same point (that a winner bonus is good because it makes changing an existing government easier):

It is the ability to “throw the bums out,” more even than the ability to choose a new government, that is the most striking practical virtue of FPTP. Our governments are responsible, must answer to the voters, and are regularly defeated. Joseph Schumpeter (1987: 272) and Karl Popper (1963 and 1988, April 23) saw the ability to get rid of an unsatisfactory government as the purpose and test of democracy and condemned proportional representation for not seeing this. To “throw the bums out” is almost impossible with proportional representation. In the 50 years after 1945 in 103 elections in Belgium, Germany, Italy, Japan, the Netherlands, Sweden, and Switzerland, the major governing party was only thrown from office six times (Pinto-Duschinsky, 1998, September 25). Major parties have remained in government for decades under proportional representation despite wide fluctuations in their votes. Minor parties often seem to share in government in inverse proportion to their electoral success, turfed out when their vote grows and they look threatening, and brought in when it sags.

As you noted below, such bonuses occur even in some semi-proportional systems, e.g. it's an intended feature of MBS. But it's also a less intended feature in SNTV. And

In his famous study of the impact of electoral systems, Douglas Rae observed that a high degree of proportionality is hardest to achieve in single-member electorates.

(of which FPTP is a prime example.) Also, an alternative name is (consequently) "winner's bonus".

Curtice notes that

The [FPTP] system will only provide the winner with a substantial bonus if a relatively large number of seats are highly competitive (or ‘marginal’) between the two parties. In those circumstances, seats readily change hands from one party to another, thereby making it likely that even a party with quite a small lead in votes will enjoy a substantial lead in seats. If, however, there are relatively few such seats, then a party might need a big lead in votes before it secures a majority of seats.

You may find of interest the paper of Shugart (2001) on "mixed-member system" (MMP). His theoretical preference is quite well laid out and contains what he considers to be the strong point of plurality systems (delivering identifiable governance):

Part of the problem is in figuring out what “society” wants. Of course, all the standard problems of social choice are inherent in any expectation that elections provide clues about collective preferences (Riker, 1982). Minimally, elections are simply a devise for determining who should govern, and not an instrument for determining what policies politicians should pursue once in office (Schumpeter, 1950). Indeed, empowering a government is a key component of my understanding of efficiency, as much as it was for Bagehot. In order to empower a government, elections must offer voters a choice from two parties or blocs of parties, one of which will be likely to attain full control of the government. I define this aspect of efficiency below as the “identifiability” of competing governmental options.

Systems based on the majoritarian pattern of democracy (Lijphart, 1999) by definition offer high identifiability, but they do not assure that the government is supported by a majority. On the other hand, systems based on proportional representation usually assure that governments are based on coalitions representing a majority of the electorate, but the government that forms is usually not identifiable in the election campaign that precedes its formation. Systems that offer very low identifiability may be termed hyper-representative systems. Pre-reform Italy is a prime example.

While necessary, identifiability is not sufficient for efficiency, because of the high disproportionality that typifies majoritarian electoral systems. Given disproportionality, the government that emerges from the electoral process might represent only a plurality and thus leave the majority utterly unrepresented in the government. Again, elections are at best “noisy” indicators of voters’ actual policy preferences, due to the problems of social choice. Nonetheless, the risk is that governments that are based on the electoral support of well under a majority of the voters will tend to pursue policies that are not favored by a majority. To put it another way, such a government is not constrained to follow more broadly supported policies because it governs alone.

I shall call systems that generate governments representing well under a majority of the electorate pluralitarian systems, thereby signaling that they are indeed not representative of a majority, due the presence of a multiparty system in the electorate. In such systems a less disproportional translation of votes into seats would almost certainly lead to a coalition government, which would be more likely to represent the preferences of a majority of the electorate, and would constrain any one party from pursuing policies that were primarily of interest to its own constituency rather than to the broader electorate. Pre-reform New Zealand is a paradigmatic case of a pluralitarian system.

Thus, within the inherent limits of elections as instruments of collective choice, the most efficient way for elections to connect government to the electorate is for there to be both high identifiability and high proportionality. However, these two key components of efficiency are likely to be in conflict. Identifiability is associated with majoritarian electoral systems and proportionality is associated (obviously) with proportional representation. It is because of these countervailing pressures that mixed-member systems are likely to be more efficient. Theoretically we can expect the tier of single-seat districts to encourage parties to aggregate into two principal blocs — generating high identifiability — and the proportional tier to moderate or eliminate (depending on specific details of how the tiers are combined) the disproportionality of the outcome. The resulting governments can be expected to be efficient in the sense that they are both empowered from the election outcome yet constrained by the need for coalitions to take in a broader swath of the electorate’s preferences.

His empirical (interparty efficiency) index he derives is not as impressive as one might hope from that. Essentially, he linearly combines an partly impressionistic measure of "electoral linkage" [L] (a measure of identifiablity) with a purely statistical plurality enhancement measure [P] (which actually works as a penalty, because the efficiency formula is L+P-1). For Westminster-style systems, the electoral linkage is basically 1, so only the deviation (from zero) by plurality enhancement counts as inefficiency.

A new paper of this kind is Raabe and Linhart (2017), which sadly uses almost completely different terminology for the roughly same notions.

Proportionality [... well, you know what it means]. The advantage of concentrated party systems, on the other hand, is that government formation is connected more strongly to the voters’ choice. In the clearest cases, one single party wins a majority of seats and forms a government – and thus can be held responsible for its performance in the upcoming elections. The more fragmented a party system is, the less clear it becomes who is an election winner and the more government formation depends on coalition bargaining between parties instead of election results. At the same time, more fragmented party systems generally lead to more parties in government so that single parties in government can be held accountable by the voters only partially (Powell, 2000). As polar design options, pure PR electoral systems are associated with highly representative parliaments that allow for a more nuanced representation of the electorate, while plurality electoral rules are associated with the creation of accountable single-party governments (Duverger, 1954; Rae, 1967; Farrell, 2011). However, PR systems typically fail to concentrate the party system in order to enable swift government formation and plurality systems fail to provide accurate representation and to account for minority interests (Shugart, 2001).

However this 2017 is far better (compared to Shugart) at exploring the multi-dimensional design space between (pure) plurality and (pure) propotionality:

We expect that the share of single-member districts, the district magnitude, the legal threshold, and the level of compensation each exert individual effects on the propensity of an electoral system to successfully provide both proportionality and concentration.

Alas, they don't seem to consider an explicit bonus system as a means to bridge the two... anywhere in the paper. (An interesting pair of factoids is that Anglo-Saxon political scientists hold MMP is very high regard, while MBS has been held in outright derision by some political scientists, and generally gets little academic attention.)

  • You describe FPTP votes as if they were one and the same with majoritarian results in the legislature, and they are closely linked, but each can exist without the other: mixed-member proportional representation has districts but no majoritarian bias; and the majority bonus system establishes majoritarian bias even with party-list voting. FPTP advantage (b), about the composition of the legislature, comes close to answering the question but does not say who came up with this theory. Sep 29 '18 at 0:30
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    @AaronBrick: you really need to precisely define your terminology. MMP is not considered majoritarian except in some publications, e.g. by Ganghof. Neither the IDEA book nor Amy consider MMP as part of the "majoritarian/plurality" systems. And what is "majoritarian bias"? Your question(s) are basically impossible to answer without settling on some terminology/definitions.
    – Fizz
    Sep 29 '18 at 0:37
  • MMP does not produce majoritarian outcomes, it produces proportional outcomes. I discuss majoritarian bias in the first part of the question. Sep 29 '18 at 0:39
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    Even if the principles are down to political folklore, this is enough descriptive material for me to work with. Thanks! Oct 1 '18 at 23:23

If I understand your question right, in the US the critics of our "Electoral College" would include proportionalists, who would prefer that elections are always decided on numeric votes. These folks would probably find the US Senate puzzling, since there isn't even the pretense of citizen-proportional representation.

I think that direct numeric representation is by no means a bad thought, but that the system we have is built upon this and also more good and worthy thoughts:

By apportioning electoral votes during the census rather than during the election, we believe that we mitigate the power of the current government to bias turnout in its favor.

Also, geographic differences such as agriculture and industry, and weather, affect both policy needs and voter turnout. The census / election method for apportioning votes prevents a New England hurricane during voting season from biasing policy against New England manufacturing for the next four years, for instance.

By requiring a two-thirds vote for certain powers of government, we insure better stability for policies that would otherwise make life difficult for people who need to make plans on a longer term than four years, such as 30-year mortgages and the 13 years of primary education for each child, for example.

American government derives its just powers from the consent of the governed, not the consent of those voters who were willing and able to vote. Theoretically then, the votes of the adults are representative of the consent that their children are too young to grant, and the votes of those not-affected by a snow storm are representative of those snowed-in. It's not a perfect situation, but we believe that it's better than the alternative.

  • 1
    The question asks for specific theories which justify these election outcomes. Can you cite some theories that match their requirements? Sep 27 '18 at 17:24
  • I'm sorry, I don't understand. In which context are these theories expected to appear? Sep 27 '18 at 17:36
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    The majoritarianism I'm interested in is why 51% of votes for Congress might, for example, win 55% of the seats. Mathematically it's no mystery, but I want to know which thinkers have defended this kind of outcome. Sep 27 '18 at 20:57
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    I respect that you think it's a good idea, and I continue to hope that there's a complementary theory out there based on established principles. Sep 28 '18 at 20:04
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    @AaronBrick I looked for one, but I'm not familiar with them so the effort fizzled. Sep 29 '18 at 3:23

I don't know what you mean by "theoretical justifications"; any such justification has to rest on some premises, and you can justify all sorts of things by just picking your premises.

Arrow's Theorem

In democratic decision making there is a big theoretical obstacle called the Arrow's Impossibility Theorem. This states that if you have three or more alternatives then there is no voting system that can convert individual preferences into a group preference that meets the following criteria:

  • If every voter prefers alternative X over alternative Y, then the group prefers X over Y.

  • If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).

  • There is neither "dictator" nor "prophet": no single voter possesses the power or the knowledge to always determine the group's preference.

This obviously applies to representative voting systems when you have more than two candidates, but it also applies within a legislature; if you put 3 alternative policies in front of a parliament there is no voting system that can consistently pick the "best" one.

A simple example of this is the "spoiler party" effect. Suppose that in the USA the Libertarian Party took 10% of the vote from the Republican Party. The result might well be an election with 47% Democrat, 43% Republican and 10% Libertarian. The 53% of Republican and Libertarian voters all disagree strongly with the Democrat platform and would all prefer the other party to the Democrats, but their preferences are overridden by the 47% of Democrats.

You might be thinking that a more sophisticated voting system, such as Single Transferable Vote, might solve this problem. But the point of Arrow's Theorem is that no solution will meet all of these criteria all of the time.


Rather than looking for theoretical justifications, I would instead look at practical issues. Society is complex, and there has to be a trade-off between technocracy and democracy. Representative electoral systems generally work reasonably well pretty much of the time and are self-correcting because the electorate can always throw the rascals out. Hence they are the preferred solution.

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    Arrow's theorem applies to any voting system. Multi-seat elections like the UK Parliament and the US electoral college (if that is what you mean) are subject to it as well. My point was also that once you have the legislature seated then whatever voting system they use to make decisions is also subject to Arrow's Theorem. Sep 28 '18 at 9:28
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    Note that Arrows theorem only applies to elections where the votes are binary. It doesn't apply to systems like range voting. Sep 29 '18 at 18:56
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    @AaronBrick Arrow's theorem says that if every voter ranks the candidates e.g. "A first, B second, C third" then there is no way to translate that to an election result that fulfils his conditions. Sep 30 '18 at 9:38
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    @AaronBrick The ranking exists in the head of each voter. A voting system discovers this ranking, or some part of it, and translates it into an overall ranking. FPTP starts by throwing away all except the first choice of each voter. Sep 30 '18 at 18:04
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    FPTP is not exempt from Arrow. Oct 1 '18 at 9:46

Boiling this question down, it seems to be asking why do people believe things like Electoral Votes are a good thing. Since that's more a matter of principle, it's not obvious that game theory really adds very much to the question.

Majoritarianism is useful. Here's two analogies:

  1. American Major League Baseball has a national championship called the World Series. The winner is the team that wins a best-of-seven playoff. The game wins are counted, (majoritarian), but not the total scores of all the games, (proportional). So if the series lasted seven games, and the scores were:

            Red_Sox     Giants  
            4           3       
      (tie) 6           6       
            1           2       
            3           1       
            2           1       
            2           5       
            4           11      
            3           2       
    Total:  25          31

    The Sox would win, even though they had fewer points than the Giants. Baseball is popular in the US, as is Basketball, (which also has a best-of-seven championship), and Hockey, (which has yet another best-of-seven championship), so it seems Americans like majoritarian contests, and perhaps that affinity correlates with the structure of America's political institutions.

  2. The general transit of information in a large nation behaves much like the transfer or conduction of heat in cooking, pottery, etc., where a large nation, when heated by the transfer of much information, is like a clay pot in a kiln. Exposing its more conservative regions, (or "colder" spots), to too much progressivism all at once, (i.e. "heat", or some very sudden loss of it), jeopardizes a nation's structural integrity, just as pouring icewater in a pot that was just baked in a kiln, (or just as pouring boiling water in a glass that's been in the freezer for an hour), would shatter it from thermal shock. Majoritarian institutions such as the Electoral College function as a kind of heat sink to help prevent warping and shock, (i.e. civil war).

    There is another way for a large nation to exist without breaking apart from such shocks, and that is to turn down the "heat" everywhere, by limiting new information, (i.e. China/Soviet style totalitarian censorship), so that the nation is generally never willingly exposed to enough new information at once as to fracture it. But large nations that try to exist in a shock-free equilibrium soon suffer from information shocks caused by nature itself -- these nations exhaust their resources carrying out seemingly reasonable plans which like most plans gradually go a bit wrong here and there, but which cannot right themselves fast enough because too much "negative" information bandwidth would disrupt their homogenized equilibrium.

  • 1. This only shows that it's used, not that it's useful. 2. Creative, but bizarre metaphor. It also misses the point, because shocks are more likely under majoritarian systems than proportional ones. Oct 2 '18 at 16:06
  • @CameronBrick, Re "shocks are more likely under majoritarian systems than proportional ones": interesting, please elaborate.
    – agc
    Oct 2 '18 at 17:08
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    Quick note: Your world series has an eighth game... the last game can be removed and the point still remains. Also your math is off as both teams only have 3 games in total. Your second game tie score would be resolved by extra innings in game, so for your math to work, Socks get one extra point there.
    – hszmv
    Oct 3 '18 at 16:19
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    Okay... yeah, I'm not much of a baseball nerd on the stats... I think they do extra innings now, because these are big media events, but it does play better to your point... Basically, it was neck and neck until game 7, when the Giants had a blow out on the points. Had we gone by score, it would have been a huge upset because up until that one game, the Socks were winning.
    – hszmv
    Oct 4 '18 at 14:24
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    @CameronBrick, Thanks. Re "...measured by the average desires of the population...": that would depend on how those averages were computed. A majoritarian calculation of public desires, (regional blocks, as with electoral votes), would provide a different result than a proportional calculation, (as with total citizen votes).
    – agc
    Oct 4 '18 at 15:59

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