<div>Here's a bunch of responses </div>
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<div>dlw:My approach replaces STV with LR Hare, I guess I don't really care whether rankings get used or not, but I do like having fewer seats with PR with a Hare Quota, so we can avoid those arbitrary percentage restrictions. It lets third parties decide who's the party-in-power but helps the party-in-power get more seats so they can get things done if they are generally popular, or able to win many of the single-winner elections. </div>
<div>KM:Personally, I think Sainte-Lague is a more proportional approach than LR-Hare. In being a divisor method, it can avoid the population-pair monotonicity problem, and by measures of proportionality, it is usually about as good as LR-Hare.</div>
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<div>dlw: SL may be more proportional, but since I'm advocating for the use of a mix of single-winner and multi-winner election rules, I have no problems with the former being biased towards bigger parties and the latter being biased somewhat towards smaller parties. </div>
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<div>dlw; In case you didn't notice, part of my pragmatism is that I don't really value proportionality in representation that much... This is why I prefer small-numberred PR rules (less proportional) that increase the no. of ompetitive elections and maintain the legislator-constituent relationship. </div>
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<div> KM:You might be able to get something more easily understood yet retaining some of the compensation part of the first version, by doing something like this: first elect the single winner/s. Then start STV with the single winner/s marked as elected (and thus with vote transfers already done).</div>
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<div>dlw:The rub here is the desirability of guaranteeing that the Condorcet winner is elected. In "more local" elections that attract less attention, I put less emph on the usefulness of rankings and thereby the Condorcet winner.</div>
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<div>KM:So the balancing point depends on how much you value single-winner balance against PR diversity. You could probably do some calculations to find out to what degree increasing the single-winner share lowers the probability of small-party kingmakers getting undue power, but ultimately, you'd have to make a value judgement.</div>
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<div>dlw: I'm intrigued by the 3:1 ratio approach for a number of reasons, including its simplicity... If a party is really popular, it'd typically get 3 of the seats and a two seat edge over its closest rival. This is half of what is the case if it's just a single-winner. If no party is really popular then the top party gets 2 seats and a one seat advantage, only one-fourth of what would typically happen...The goal being: a meld between the de facto current system in countries like the UK and a EU-style PR system...</div>
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<div>dlw: 1. While all forms of PR fall short of proportionality in representation, the best predictor of proportionality is the number of contested seats. </div>
<div><br>KM:Only if there are enough parties to provide competition within all the seats. If you consider a district that has 20% leftist voters (for instance), if there's only one left party, then 20% of the seats (up to rounding) will tend to be held by the leftist party. Not very contested; and even if you get multiple leftist parties, these will not affect the extent to which the right-wing seats (say) are contested.</div>
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<div>dlw: I didn't mean contested in that sense, I meant how many seats total were in the ele</div>
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<div>Rounding may also amplify the apparent contested nature of the seats. Say that a district has only two viable parties, and they're even - 49%-51% of support for each party. Then if you have single-member districts, in times of 55% support for the first party, most of the seats will go to the first party, and in times of 55% support for the second party, most of the seats will go to the second party. Thus all seats appear to be contested. Yet, with PR, each would get about half of the seats, and some marginal seats would shift back and forth. That would seem less competitive, but nothing about the popular support for each party has changed: only how the seats are allocated has been.</div>
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<div>Yet, PR with fewer seats induces more turnout than PR with a greater<br>numbers of seats. So the election rule that gives us proportionality<br>tends to make it so there are fewer competitive seats and less<br>uncertainty about election outcomes and consequently lower voter<br>
participation.</div>
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<div>The Hix-Johnston-MacLean document states that these effects are weak. To quote:</div>
<div>"Turnout is usually higher at elections in countries with PR than in countries without, It also tends to be even higher in PR systems with smaller multi-member constituencies, and also tends to be higher where citizens can express preferential votes between individual politicians from the same political party rather than simply choosing between pre-ordered party lists. In general, the more choice electors are offered, the greater the likelihood that they will turn out and exercise it. However these effects are not particularly strong, there is some evidence that highly complex electoral systems suppress turnout, and turnout levels may partly reflect influences other than the electoral system, for instance in some countries voting is compulsory."</div>
<div>So I don't think you can necessarily draw that conclusion. The apparent competitiveness between seats may be lesser (because of what I mentioned above in that single-member districts are much more win-all/lose-all), but that doesn't mean the real change in voter opinion from term to term is any greater in SMD countries.</div>
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<div>2. Proportionality in representation does not entail proportionality in power and the latter is desired more than the former. As such, it seems that minority dissenters will need to use extra-political methods (not unlike #OWS) to move the center, regardless of whether PR or another mixed system is used.</div>
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<div>Proportionality in representation is correlated with proportionality in power. The correlation isn't perfect, as Banzhaf and Shapley-Shubik's measures make apparent, but to leap on that and conclude that proportionality isn't proportional... that's unwarranted.</div>
<div>If anything, when proportional representation disagrees with proportionality in power, the power favors the minority parties. Minor party kingmakers can make themselves costly if they know there won't be any coalition without them. Hence the presence of thresholds in most PR systems: these keep too minor parties from becoming potential kingmakers.</div>
<div>Over here, the threshold of 4% keeps most "swing parties" (as one may call them) out of power. Yet the threshold is soft - even parties below 4% of the total vote can get representatives, they just don't get MMP-esque compensation on the national level. (Our PR system is a bit unusual in this respect: parties get additional seats if their per-region seats reflect their national share of the vote too badly.) Perhaps you'd want a hard threshold for a less homogenous country, but my point is that the problem can be managed.</div>
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<div>3. If both PR and single-seat elections are in use and the latter favors bigger parties then does PR need to be perfectly proportional or could it be biased somewhat in favor of smaller parties? Might not the opposing biases tend to cancel each other out?</div>
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<div>That's somewhat the idea of MMP. In MMP you have a local election rule and a PR rule. Usually the local election rule is Plurality and the PR rule is party list, but you could use any combination. Schulze has suggested using Schulze STV for a "deluxe" form of MMP - see <a href="http://home.versanet.de/~chris1-schulze/schulze4.pdf" target="_blank">http://home.versanet.de/~chris1-schulze/schulze4.pdf</a> for more about that.</div>
<div>So, yes, if you use both single-seat and PR in the same country without linking the two in some manner, the bigger parties will tend to acquire a disproportionate share of the seats when seats elected by both methods are considered as one group. To fix this, you can add feedback between the types (MMP), or just accept the disproportionality (parallel voting).</div>
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<div>These seem to imply that we need not strive for proportionality in representation as the gold standard for electoral reform. If the two major parties, with a somewhat disproportionate amount of representation, are more dynamic then they'd tend to represent well the majority of the population and heed minorities that frame their issues respectfully. </div>
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<div>Do note, though, that the same Lijphart as you referenced on your page, said:</div>
<div>"If partisan conflict is multidimensional, a two-party system must be regarded as an electoral straitjacket that can hardly be regarded as democratically superior to a multiparty system reflecting all the major issue dimensions." ("Democracies: Patterns of Majoritarian and Consensus Government in Twenty-One Countries", 1984, page 114.)</div>