Talk:Mixed-member majoritarian representation

Distinction from parallel voting

Is this distinct enough from parallel voting to deserve a separate article? I know they're not technically the same, but it seems like these could be merged. Closed Limelike Curves (talk) 17:38, 13 July 2024 (UTC)

Don't think it should be merged. Yes, there is a 90% overlap if looking at nationak legislatures, but nowdays there are so many mixed systems in use, I think both categories deserve their own article, although both need more than just polishing.

Mixed member majoritarian - it's good that it exists ad it provides contrast to MMP, this distinction is common in literature, especially newer, so this should definitely be kept

but it also covers other systems, especially in Massicotte/Blais typology:

-coexistence - where many districts use majoritarian while others proportional, this is enough to make it not proportional, definitely fits here and nowhere else (this is not parallel voting)

-parallel voting with a winner-take-all and proportional mix. yes, I dislike the phrase "majoritarian" here too, but I haven't really seen the "winner-take-most" anywhere, and is actually somewhat more confusing in my opinion

-majority bonus/jackpot (fusion) - has it's own article (probably should have two different ones as well), probably the most perfect fit for MMM (since here majoritarian is more appropriate here)

for all these I would stick with MMM being an article

-systems with very limited compensation, which are technically not parallel, but for all intents and purposes are surely not MMP either (Korea, Mexico, etc)

Parallel voting

-just means two independent systems superimposed (superposition) on each other. Sometimes even just the two-vote version.

-it could be two proportional systems too

I would keep the parallel voting article, especially since its even a bit more polished already.

I think if AMS and MMP are still separate (which I am neutral on), I think these have so much more reason to be. Rankedchoicevoter (talk) 20:02, 14 July 2024 (UTC)

I think that makes sense (keeping both separate if we keep AMS/MMP separate), but I feel like the Wikipedia articles on all these systems are kind of a complete mess, and I have no idea what's going on or what's different between these systems. I have no idea what , and it would be very nice to have a diagram or categorizing proportional representation systems by all the axes they can vary along. Something like:

1. No list (e.g. PAV) vs. Open list vs. Semi-open (quota) list vs. Closed list
2. Mixed single vote vs. Two separate votes
3. Homogenous vs. Mixed-member compensatory vs. Mixed-member noncompensatory
4. Single apportionment vs. independent regional apportionments vs. biproportional apportionment

I've mentioned before that I come from a math/social choice/econ background, so I don't know much about detailed terminology on all these systems.

I think someone has to be trolling me. Have politicians really created a hellish series of Rube-Goldbergesque contraptions specifically to torment me? Dear god, what in the fresh hell is going on with the German Bundestag? How did it get so big? Wait, half their members are elected by first-past-the-post? You can just keep the overhang seats? Well, at least they compensate for it by adding... wait, they used to not have compensatory seats?! Closed Limelike Curves (talk) 23:32, 14 July 2024 (UTC)

I empathize a lot. I'll see what I can do to clean it up a bit.

I would actually be up for ditching MMM (especially because of the "majoritarian" in it) but only if we can ditch MMP (which is not really that proportional often...)

I see that you renamed a few articles with lesser used but more accurate names. We could do the same here. Then it would look like this:

Mixed compensatory systems:

-"MMP", with all it's forms

-currently german system??? (idk if still counts as "mixed")

-AMS

-DMP

-majority jackpot?

-vote linkage

(-supermixed systems with partial compensation)

Mixed non-compensatory systems (sometimes called mixed majoritarian).

-parallel voting with winner-take-all + proportional setups =?= "supplementary member system" = "trench system"

-seat linkage (copying?) like Pakistan and some other countries where additional (often) womens seats are added but in proportion of FPTP seats

(mention of partially compensatory systems)

-majority bonus

potentially: Mixed partially compensatory systems

-supermixed

-vote linkage, scorporo Rankedchoicevoter (talk) 08:25, 15 July 2024 (UTC)

Seems interesting! I'm generally wondering whether we can describe some of these methods as "compositions" of different traits. e.g. most "majority bonus" systems (at least the Greece-style ones) could be reinterpreted as parallel voting, where some of the seats are elected by party list block voting and the rest by proportional representation.

To give an example of something I'm confused about, what's the difference between vote linkage and seat linkage? These sound like they have to give the same results, but I'm kind of confused as hell.

It seems like lots of systems that have been labeled as "different" might actually be the same. For example, is Scorporo just badly-designed dual-vote MMPR? If you let parties keep their overhang, and have a dual-vote system, you can break proportionality with the decoy list tactic. But the weird results don't seem related to any kind of "negative vote transfer" or anything like that, just the fact that they didn't make a credible commitment to introduce as many leveling seats as necessary to ensure proportionality, the way Germany does. Closed Limelike Curves (talk) 15:26, 21 July 2024 (UTC)

To answer these 2 points:

1. Majority bonus (and jackpot) - I would say this is where the "mixed member majoritarian" or "winner takes most" is certainly applicable, it kind of the idea in it's purest form. But often when I see articles about mixed systems, they focus on the two tier "mixed-member" systems, which are usually the ones also mixing personal and list, and local and at-large representation (with many varied exceptions though). But yes, these are mixed systems as in combining winner take all party block voting and proportional list voting. Also they are one of the most clear "semi-proportional" systems another term seemingly out of fashion. But to call them "parallel voting"? I would need a few sources for that, have not encountered. As far as I know, with parallel voting the following are key features:

-2 tier (not by default with majority bonus), so not "coexistence" on the same tier

-typically one personal, one list vote (majority bonus is for lists)

-typically FPTP + list-PR, but not always, can be two winner take all or two proportional systems

-the combination is independent, so no seat or vote linkage. Also called the trench system in German and supplementary member (SM) system in English (which is very confusing since "additional" means the same as "supplementary", in fact, I would say supplementary sounds slighly more like it would be the compensatory one, but no: additional member system is basically MMP, while supplementary is parallel... I think this chaos comes from different branding in different countries. In Britain MMP is AMS, and there's no talk of SM/parallel. In New Zealand MMP is MMP and parallel is SM, which was considered)

-independent should also in theory mean there is ticket splitting available, that's why it's parallel - but then what is Italy? there ticket splitting is not possible or only between parties of the same coalition or something. I don't fully get it. So it's not exactly independent, but otherwise parallel. No compensation. Same with single vote SM... I don't know, there are just so many variants. So I would keep to the definitions above, with majority bonus being mixed, but not filed under parallel voting, it seems too different on multiple criteria (mainly the tier thing though).

2. vote linkage and seat linkage? These sound like they have to give the same results - this is a deeper one again, and unfortunately it doesn't

mostly only seat linkage is known, it's the usual MMP setup. It doesn't just converge, but goes to proportionality with every extra seat if there is no decoy list shenanigans. It's compensation to list vote results.

vote linkage is somewhere between seat linkage and the single/dual vote "supplementary member" system, but it's neither. It's taking some votes, but not all and using those or adding/substracting to/from another set of votes. They call it "compensation" because it doesn't use all of winners votes (or any), but it doesn't converge to proportional. If you don't have enough seats, which is usually the case, it is not much compensation in fact it adds additional "overhang seats" which MMP would never do. If you have the perfect amount of seats, might be proportional (not sure about that with more than 2 parties and independents...), and if you have too many seats it overcompensated, which would not happen under MMP. Daniel Bochsler has a good paper on this.

So yes, scorporo and relative are kinda badly set up MMPs, but also not really, since they would basically never have proportional outcomes. At least with AMS, MMP without flexible seats it is known that within a range of possible results, it makes it perfectly proportional (maybe excluding independents).

But, again this is from the Bochsler paper:

-MMP has the decoy list tactic, which scorporo has too because of the vote subtraction. But vote transfer alone doesn't have this, if the transfer votes are just simply used on their own or added to the parallel vote (both in use in Hungary, formerly in Germany where it was used instead of MMP in British occupation zones).

-"positive vote transfer" has a theoretical stronghold split tactic, I don't know if it has been observed empirically.

-any vote transfer with too many compensation seats has an incentive too lose (was never the case in reality they always use too little)

So yes, it's confusing and should be differentiated better, but it doesn't help when some sources categorizing parliamentary elections in countries just lump in Hungary as "MMP" or "parallel" when it's neither (but I guess it's MMM at least), or say Italy is "mixed" (but is it parallel or what?), or and all of these terms are just used interchangeably. Rankedchoicevoter (talk) 09:43, 22 July 2024 (UTC)

As far as I know, with parallel voting the following are key features

Hmm; I've seen "superposition" and parallel voting described as synonyms. Going off the etymology/words themselves, it should mean any system using a mixture or superposition of two electoral systems that run "in parallel", i.e. with no interaction between the two. In other words, the final results are come from concatenating/adding together the individual results of each component.

That said, if superposition and the specific mixtures you're describing have been conflated for a long time, things might have gotten so confused by now that nobody has any idea what any of these words mean anymore, and there's only a tangential connection to the etymology.

In large part I'm hoping to fix this kind of logical confusion and conflation, by splitting electoral systems into logically-distinct parts. For instance, FPTP strikes me as a very awkward article, because it conflates the concepts of a first-preference-plurality vote and single-member districts (even though SMDs can use any single-winner system). Closed Limelike Curves (talk) 18:49, 12 August 2024 (UTC)

From the only sources where I've seen superposition, it meant parallel voting. Etymologically, either superposition or parallel voting may be imaginable for the other two independent combination, coexistence and fusion, since in some way those are also implying that two systems work in parallel to each other in some way. But unless there's sources saying that coexistence or fusion (majority bonus) is also superposition/parallel voting, I wouldn't use it in this way. Maybe this is just me reading to much into, but the idea is that fusion is not superposition or parallel, because its on the same tier (so not superimposed vertically, nor placed next to horizontally, but it's kind of fused together in the same thing - granted not all the majority bonuses I saw when adding to those articles really fit this so clearly anymore) and it's not parallel because there no parallel voting (then again, can single votes be parallel, or following the metaphore it that "diverging vote"? also some majority bonuses use 2 votes). And coexistence is not superposition or fusion because it's not vertical but horzizontally next to and not in the same district, and not parallel again because for one voter theres no parallel voting, each voter votes in their own district. With parallel voting for each individual it's parallel voting they have influence in both tiers, while in coexistence, only one.

The FPTP I see but probably not the place to discuss it. But I understand that much of that article also discusses the consequence of SMDs, since that is often how it's used when its not just used for a single winner but an assembly. Rankedchoicevoter (talk) 21:48, 12 August 2024 (UTC)

I'm a bit confused as to what fusion is supposed to be, actually. The definition isn't clear to me like it is for coexistence, parallel, or compensatory systems. Closed Limelike Curves (talk) 02:39, 13 August 2024 (UTC)

Fusion is definitely majority bonus. So there let's say there is one district in the whole election with 100 members. 50 of them are given to the plurality winner list, the rest are proportional. So that's mixed-member majoritarian in the broad sense for sure, in fact MMM is a better name for that than for most versions of parallel voting (possible electoral inversions and such). But its not coexistence, because that would mean there are more districts with different voters, even if you say the two 50 seat pools are like two districts, not really, because different districts have the same voters, which is not the case. It is also not superposition/parallel voting (in the sense Massicotte uses it), because it doesn't have too tiers (and maybe less importantly, it doesn't have two parallel votes). Also, it cannot be conditional or compensatory since there's not interaction between the two tiers whatsoever (expect that the use the same exact votes), the winner-take-all bonus is not impacted by the proportional distribution, its simply awarded to the plurality winner and the proportional distribution is not impacted by the giving the bonus to any party. So fusion is the simple majority bonus.

I think the correction(compensation)/conditional/coexistence/fusion/superposition (+supermixed) is a the best framework for sorting these as of now, much more accurate than the MMM and MMP thing which are is not only used too, MMM is super misleading (majoritarian/winner-take-all, "majoritarian" when it semi-proportional by definition... I think it's on point as a brand to give across the effects (they do win huge majorities easily under MMM), but not on point theoretically) and MMP is sometimes used for systems that are nowhere near proportional, just because they are compensatory. Hungary is a good example, so many aggregations list it as "MMP" just because they don't have that many categories, but if you look at how it works and the results, it's obvious that while it has a it of compensation, it's basically almost just parallel voting, MMP is just very misleading. But I don't think the term MMP will be abandoned anytime soon, until then MMM will have to be there to contrast as an opposite.

But you asked about fusion, so I think the simple majority bonus is the pure example for fusion. The problems start that as far as I know, the only country with a majority bonus on a national scale is Greece, but there the bonus is used on a national level, while most of PR is in multi member districts. So it has two tiers, but the opposite way to the typical FPP+PR (MMM) parallel voting: proportional is (mostly) local, winner-take-all "district" is national. I think this means its supermixed: fusion+superposition (system is newer than source to go on)

Then there is the majority jackpot: It's clearly differentiated from fusion (majority bonus) because it conditional, while bonus is unconditional (independent combination):

Pure conditional is like this: "If leading party has a majority, winner-take-all. Otherwise, PR-D’Hondt" (Massicotte 1999). Problem is this is not the typical majority jackpot, and its not differentiated, I think technically the common majority jackpot, something like this: "If leading party has a majority, winner-take-all. Otherwise, leading list gets half of seats, other half distributed by PR among other parties". This is also conditional (if-otherwise), but its also fusion (half for winner, half PR), but its also correction ("other" parties). Its not a bonus, its a jackpot, seats outside the jackpot are not PR, but PR for the other parties. Under bonus (simple fusion), the winning party would also participate in the PR.

So majority bonus: fusion

Winner-take-all or PR depending on majority (I guess this counts as a type of jackpot too): conditional

Common majority jackpot: conditional+fusion+correction (supermixed)

More complex majority jackpots (two round or supermajority clause in case of 50%+): double conditional + fusion + correction (supermixed) Rankedchoicevoter (talk) 06:55, 13 August 2024 (UTC)

So, do majority jackpots and bonuses only kick in if you get >50% of the vote, or do they work for any party winning a plurality? I think we can safely classify jackpots as conditional. From my understanding the method is:

1. If the leading party has a majority, assign them X seats, then assign the rest of the seats proportionally (with compensation).
2. If no party has a majority, assign all seats proportionally.

Which would make jackpots a weird kind of (partially) compensatory system.

It is also not superposition/parallel voting (in the sense Massicotte uses it), because it doesn't have too tiers (and maybe less importantly, it doesn't have two parallel votes).

What do you mean by "tiers" here? Do you mean two different kinds of MP (e.g. list vs. directly-elected)? Or do you mean a mixture of seats assigned by different methods?

The reason I think e.g. Greece's plurality bonus system is a superposition is it combines two different apportionment methods which don't interact. One set of seats is elected by proportional representation, while the other set is elected by general ticket. Closed Limelike Curves (talk) 02:08, 20 August 2024 (UTC)

Yes, I agree, I think jackpots are inherently not only conditional but fusion and compensatory too, even though it's weird to say since jackpots are larger and seem more winner-take-all.

A bonus is simple fusion: assign 50 seats to largest party, assign rest to all.

jackpot is as you said, has the condition, one branch has the bonus (fusion) but then a compensation too

Theoretically there are non-conditional compensatory bonuses (fusion+compensation): Assign leading party X seats, then assign the rest of the seats proportionally (but not the leading party, so with compensation), even if they get more than X proportionally (or have a majority, whatever the condition would have been).

And also conditional non-compensatory bonuses (conditional+fusion): If no majority, assign leading party X seats, then assign the rest of the seats proportionally (without compensation), otherwise PR

I think the Greece is not compensatory, but it has pretty much every other type of mixed system in it (https://en.wikipedia.org/wiki/Apportionment_in_the_Hellenic_Parliament):

-Coexistence (9 local MPs by first-past-the-post, rest in PR)

-Fusion (within nationwide MPs, there are PR and winner-take all formulas, some PR seats, and the bonus seats)

-Superposition (local PR and national bonus technically superposition, but maybe not really "parallel voting" if there's no two votes. But there's also local FPP and national PR seats so it's double mixed in this way)

-Conditional - this might not be the case any more but I think the plurality bonus only kicks in after 25%, but and it increases to 50 seats gradually for every 0.5%. This would make it very conditional I think.

So Greece is supermixed, but not compensatory as far as I know.

By tiers I mean local and national tier. So a normal bonus all seats are national or all seats are regional, and within the national or regional district there are bonus seats, thats fusion (same district). Multiple tier (national, local, regional, etc) on top of each other are superposition. Of course, superposition can be two PR systems and then it's not considered mixed (otherwise a lot of european PR would be mixed too), but if the lower tier is FPP and upper tier is PR, then it is superposition, whether it's one vote or not. Of course, technically the MMP style compensation is also superposition, but in the literature it's not said to be so since superposition is only the independent combination, while compensation is dependent. But technically if the Greece system would be so simple that local PR + national bonus, then I would say Greece is simple superposition, not fusion (+not conditional/coexistence either) Rankedchoicevoter (talk) 07:40, 20 August 2024 (UTC)

OK, I think I'm starting to understand the distinction you're drawing between fused and non-fused systems:

1. Fusion involves using a single mixed electoral system across all districts (e.g. 2 MPs in each district are assigned proportionally, and the last MP is apportioned by FPP)
2. Non-fused systems (whether compensatory or not) elect different groups of seats at different geographic levels (e.g. assigning a nationwide bonus).

Is this correct? – Closed Limelike Curves (talk) 03:12, 28 August 2024 (UTC)

Yes, I would say the distinction is whether the two formulas are used in the same district. If yes, it is fusion (as you say, in my opinion whether it's also conditional or compensatory too, it is still fusion)

Two formulas in same district: fusion

Two formulas on the same level, but dependent on what district: coexistence

Two formulas independently on different levels: superposition

Two formulas dependently but unconditionally: correction

Two formulas where there is an "if": conditional Rankedchoicevoter (talk) 08:01, 28 August 2024 (UTC)

This is a great explanation, thank you! In that case, are superposition and compensation mutually exclusive with fusion, or does fusion describe an independent trait?

I'm thinking the way we can organize this is into independent traits, rather than attempting an exhaustive categorization of every combination of traits (which will take us to the heat death of the universe, thanks to the curse of dimensionality). Here's an attempt at organizing these into a trait system, which would let us cover most common mixed systems using only half a dozen articles:

• Article on piecewise/conditional systems
• Article on tiered electoral systems (non-fusion)
• Article on mixtures between different districts
• Article on components are independent (parallel/superposition), contrast:
  • Article on components are dependent (compensatory)
• Article on single vote vs. dual (candidate/party) vote systems
• Article on vote vs. seat linkage (? maybe)
• Flexible-size (leveling seats) vs. fixed-size

Every combination of these components should be theoretically possible (which means they're independent), even if they might be a bad idea. Then we can describe systems by mixing-and-matching these traits for a concise description. For example, Germany used to use two-tier dual-vote compensatory seat-linkage. (I think.) This classification should handle every common mixed system with only 7ish articles (8-9 if you break some of the bigger ones in two), instead of 2^7=128 (likely to confuse everyone). – Closed Limelike Curves (talk) 01:52, 2 September 2024 (UTC)

Yes, I agree. I think fusion is another trait if I understand the framework correctly.

This matches mostly with what I was trying to do recently, but you have to take into account the main systems that many people know under certain names.

Article on piecewise/conditional systems: There is an article on conditional as a draft (under the same name as where the sidebar points). It will probably be short, but it could be expanded with the same concept in non-mixed systems.

Article on tiered electoral systems (non-fusion): I don't think we need this at the moment. It is mostly the main article on mixed systems since most mixed systems are tiered. But you can make an article but then I suggest it should be about any multi-tier system, so multi-tier PR and winner-take-all too.

Article on mixtures between different districts: There is an article on coexistence, to be improved. I made it so its the concept of coexistence, it doesn't have to be about only mix of winner-take-all and proportional, it can be coexistence of two proportional like RUP, etc.

Article on components are independent (parallel/superposition), contrast: Article on parallel voting. Again, it's a trait of any system, not just WTA+PR

Article on components are dependent (compensatory): Article on compensation, also written as a trait/element. It can be expanded on vote linkage (relate it to STV) and leveling seats. Maybe even the leveling seats article can be merged in since theres two definitions of leveling seat, one is the extra flexible one in forrmer german MMP, the other is the fixed one in multi-tier PR

Article on single vote vs. dual (candidate/party) vote systems: Mixed single vote article mainly. Two different forms of "dual vote" are discussed in MMP and MBTV articles

Article on vote vs. seat linkage (? maybe). The article on vote linkage is almost ready. Seat linkage is kind of just the MMP article.

Flexible-size (leveling seats) vs. fixed-size. Maybe... currently flexible size is really just in MMP as far as I know.

I think that covers it. Now as for other categorization and confusion with specific systems.

-MMM vs MMP. It's more commonly used than the trait system. MMM page can give an overview of such systems but highlight how these can be fusion (majority bonus), parallel voting, insufficient compensation, coexistence (where it's major influence, one FPTP seat of 100 doesn't cut it) etc. And MMP article is then about fully compensatory systems.

--What is a problem here is that New Zealand, as an English speaking country refers to their system as MMP, which slightly conflates the representation category with the specific implementation where you add back overhang seats, but don't actually have all the leveling seats you need, so not fully proportional.

-AMS. Now it's kind of a duplicate of the MMP article. One thing that could be done is to cut it down to just the UK ("it's a seat linkage compensatory system used in the UK"). Say its "the (UK) AMS" system, purge references to "an AMS" system (as if it were a type like MMP) and replace it with "a seat linkage (compensatory) system". In the article, you can say the UK AMS system sometimes produces "MMP" results, sometimes it's between MMP and MMM. With a bit of research of actual results in Scotland and Wales.

(maybe it's harsh but honestly, the additional member system is such a bad name since it's not clear that it's compensatory, and the supplementary member was the name used to contrast MMP and parallel voting, and supplementary and additional mean the same thing as far as I am aware, with supplemental sounding more compensatory than additional, which sounds more parallel)

--AV+. Similar to AMS, but could even be merged

-scorporo. The same as AMS but for vote linkage. It's one instance of vote linkage, but not really a category, maybe only a category as in it's the one subtracting votes instead of adding them. So it's just about the Italian twin systems for Senate and Chamber - mention of South Korea purged, Hungary only tangentially can be mentioned. Also check is other articles say scorporo is "an AMS" system, and also it should be just barely mentioned in the problems with two vote MMP section of the MMP page.

-majority jackpot. Fusion can be the same article as majority bonus, but majority jackpot has a bit more history, I'd leave a short article about such systems, so it doesn't just appear under "conditional", "fusion" and "compensation"

-specific notable proposed systems, like RUP and DMP have their own articles, but they still can be mentioned in their respective traits.

Let me know if I missed something or how you would modify Rankedchoicevoter (talk) 08:11, 2 September 2024 (UTC)