From "The Electoral Sweet Spot: Low-Magnitude Proportional Electoral Systems"
American Journal of <political Science
https://onlinelibrary.wiley.com/doi/10.1111/j.1540-5907.2010.00495.x
This excerpt is just the conclusion:
Conclusion: Small Multi-member Districts Are Best
With the spread of democracy across the world in the last few decades and with more and more established democracies tinkering with their electoral systems, we can identify the nature of the trade-off between inclusive representation of citizens’ preferences and accountable government more accurately than we have been able to before. With this aim in mind, our results suggest that practitioners who seek to design an electoral system that maximizes these competing objectives are best served by choosing multi-member districts of moderate magnitudes.
Consistent with the traditional view of electoral systems in political science, we find that SMD systems tend to produce a small number of parties and simpler government coalitions, but also have relatively unrepresentative parliaments. On the other side, electoral systems with large multi-member districts have highly representative parliaments, but also have highly fragmented party systems and unwieldy multiparty coalition governments. In contrast, electoral systems with small multi-member districts—with median magnitude between four and eight seats, for example—tend to have highly representative parliaments and a moderate number of parties in parliament and in government.
On the representation side, our results suggest that increasing the district size from one to around five reduces the dis-proportionality of representation in parliament by three-quarters and reduces the ideological distance between the median citizen and the median government party even more sharply. This is a result of both the greater opportunities for medium-sized parties to win seats and the new incentives for supporters of small parties, who may simply prefer to “throw away” their votes under SMD elections, to coordinate into medium-sized parties. Increasing the district magnitude beyond six does not improve representation much further. On the accountability side, meanwhile, increasing the district size from one to around five increases the number of effective parties in parliament by around one, and increases the number of parties in government by about a half. Countries with small multi-member districts are more likely to have coalition governments than countries with SMDs, but these coalitions are likely to be between two or a maximum of three parties.
Put another way, low-magnitude PR simultaneously fosters inclusiveness and limits the political unruliness high magnitudes invite via party system fragmentation and coalition complexity.
In closing, it is also worth noting other research that points to an advantage of low-magnitude districts for the accountability of individual legislators. Carey (2009) describes a trend in electoral reform toward systems that allow voters to cast preference votes for individual candidates, and notes that voters overwhelmingly choose to exercise the preference vote when given the option. Yet the promise such open-list systems hold of individual accountability is conditional on limited district magnitude. In high-magnitude elections, open lists confront voters with a bewildering array of candidates (Samuels 1999), whereas low magnitudes curb both party system fragmentation, keeping a lid on the number of lists, and the number of candidates per list.
As a result, voters under low-magnitude open-list systems are better able than those in other systems to identify and hold their representatives accountable. Chang and Golden (2007), for example, find that corruption is lower in countries with open-list than with closed-list proportional representation, provided that average district magnitude is below 10, whereas at very high magnitudes (above 20), open-list systems are associated with more corruption. Hence, low magnitudes make it possible to combine candidate preference votes and individual accountability with proportionality and partisan inclusiveness.
In short, legislative elections work best when they offer opportunities for multiple winners, and thus afford voters an array of viable options, but at the same time do not encourage niche parties or overwhelm voters with a bewildering menu of alternatives. The evidence from a wide range of indicators all points toward low-magnitude proportional representation as providing a good balance between the ideals of representation and accountability.
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Here's my comments:
Concerning the article The Electoral Sweet Spot:
the author gives this rationale for why strategic voting is less under MMDs with 6 seats: political scientists of electoral systems have recognized for some time that strategic, or “tactical” voting, diminishes as district size increases, primarily because estimating how marginal votes will affect outcomes is more difficult as the number of seats, and contestants, rises. In higher-magnitude elections, shared expectations about candidate and party viability are less widely held, and therefore voter coordination around such expectations is more rare ..."
Not mentioned is this: strategic voting is less done because (as the author had previously stated) parties with 10 percent of support usually get some representation where District have 6 seats give or take so voters supporting marginal parties have good chance of seeing their vote used to elect someone even if placed on that marginal party. I think it is not so much that votes cannot calculate who has best chance of being elected - it is that many parties have a good chance of being elected so voter can take chance on voting for whom they truly want to see elected. it is directly tied to the higher rate of effective votes, represented voters under PR compared to FPTP. And - obviously as a ER-ite- I query the author's statement that SMD as in UK produces high measure of accountability. If a majority of voters did not vote for the successful candidate, as often happens in any FPTP election, then how can there be accountability? Only if the approx. 34 percent of voters (sometimes 18 percent/sometimes 64 percent or more) who elected the member abandon the member will the member not be re-elected. So who exactly wields the accountability hatchet under FPTP? in many cases it is not the majority of voters, it seems, cause they did not elect the member in the first place (in many cases). The essay is questionable but here's interesting mathematical presentation of diminishing returns of larger DM: "...Figure 3 illustrates the effect of district magnitude on the disproportionality of an election, with predicted values derived from Model 2. There is a rapid decline in the level of disproportionality of an election as the district size increases beyond 1, and then a flattening out of the relationship as the district size increases beyond 5 or 6. For example, the average level of disproportionality in SMD elections is 11.9, while the average in small multimember districts (with a median magnitude of between four and six) is 5.3. Then, increasing the size of the district beyond this does not improve the representativeness of a parliament much further: the average score for a median district size of between 7 and 10 is 4.6, for a district size of between 11 and 20 is 3.5, and for a district size of more than 20 is 3.0..." So it turns out that what is about the usual DM of STV is also the "sweet spot" for PR of all types, it seems. (I should point out that the sample used to determine the stats includes Ireland which uses STV (Dail Eirean DM 3 to 5).) STV usually involved/involves DM of between 3 and 8, although even DM of 21 is not unheard of. (Aus. NSW) I think Winnipeg's use of 10-seat district to elect its MLAs, 1920-1949, is one of the largest-DM STV elections ever in the world, up to 1990s. (and it worked well for many years - without computers!). Quota (Droop) moves quickly at lower levels and changes much slower once past 6 DM. DM 4 quota is 20 percent of valid votes DM 5 quota is 17 percent of valid votes DM 6 quota is 14 percent of valid votes DM 7: quota is 12 percent of valid votes DM 8: quota is 11 percent of valid votes DM 9: quota is 10 percent of valid votes DM 10 quota is 9 percent of valid votes DM 11: quota is 8.5 percent of valid votes. ... DM 21: quota is 4.5 percent of valid votes Quota does not determine all winners under STV but it is guide to the proportionality of the system. Quota is not used in systems that use Saint Langue I think, but according to the article, increasing proportionality of all PR systems slows after DM 6, which the list of Droop quotas, shown above, shows in concrete terms. A PR system that uses all the votes of the nation as a whole is different than one where votes are divided among districts/regions or provinces (constitutional requirement in Canada for federal elections). A party with wide but shallow support is not likely to succeed in a district-ed system. A party that has consistent ten percent of support in every city and province would get no seats in a system that uses districts with DM of 8 or less (where no overall top-up). Luckily, things are not as normal as that across Canada. A party with ten percent average likely gets as much as 30 percent or more in some places. If that peak is just in one province, the party may take ten or 20 seats under FPTP but nowhere near the 38 that is its proportional due under PR. Let's note that: 1. in Canada we have parties that do not run across the country so for them it does not matter if PR is conducted separately in each province as one province is all that matters - they have no support across provincial boundaries that they wished they could pull together. 2. Other parties are fairly consistent across provincial borders (or at least not as inconsistent as seat counts currently pretend them to be) 40 percent of the vote is the same in every province across Canada as per recent elections 40 percent of the seats in each province proportionally would have same blend of Conservative, Lib, NDP and Green. this is definitely not the way it is when under FPTP we have one-party sweeps of whole provinces or regions. 3. even if at absolute minimum, Canada must be split into ten MDs (plus three SMDs (the Territories)), four of the provinces each have more than a seventh of the seats, Ontario having almost a full third, Quebec having a full fifth, so that the great proportionality of those four means that overall the result would be very P. even if there is no overall Proportional mechanism. ========= The article, what I read anyway, does not indicate the problem of large ballots. giving voters a choice of more than 50 names would be (or thought to be) brutal but that is what would happen if more than say ten seats are up for contest. marking preferences is made easier by use of party ID and the ballot being organized by party. and in many cases voters do not have to mark a set number of preferences -- they only mark as many as they want to. But ballots can be massive under STV if DM is large. not so bad in Ireland say Carlow where 14 ran for the five spots. Edmonton -- when it had STV, in 1955 it elected 7 MLAs and there were 30 names on the ballot But then we have an election where DM was 21. NSW Aus 2021 -- there were about 350 candidates running for the 21 seats. a party ran as much as 21 candidates although no way it would win all the seats - no party won more than 7 seats. other than limit of 21, there was no restraint on the slates, parties apparently trusting in the transferability of the votes and voters' disciplined marking of back-up preferences. So no reason to worry about votes being wasted by a broad slate. But such a large ballot is definitely jaw-dropping. if there are problems with large DM, large ballots is one of them, but party-list PR may reduce this problem -- there are only so many parties. But then you definitely have problem of accountability - if voters do not vote for candidates, then how to punish a candidate you don't like without punishing a party you like? on another tack, if there is lack of accountability under PR, it is that a small shift in votes means a small shift in seats -- and only a small shift no more than that --- but also no less (generally). This is unlike FPTP, where a small shift in votes may mean great change in the elected rep. but it can also mean no change at all or only a small change. so FPTP does not give us a dependable accountability. In Alberta, Conservatives were elected to majority government from 1971 to 2015, whether it got 62 percent of the vote (as in 2001, when it took 76 percent of seats) or 45 percent as in 1993, when it took 61 percent of seats. is that any kind of accountability?
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