Juho wrote:

This is a very interesting real life example on how such "horizontal" preference orders may impact the elections and strategies in them.

Do you have a list of the strategies/tricks that are used?

One trick that appears, as has been mentioned in other posts here, is vote management. In vote management, parties aim to make voters vote for each party candidate so that the accumulated strength is nearly the same, minimizing the chance that any get lost or go to other candidates.

Schulze wrote about vote management strategies at [ http://m-schulze.webhop.net/schulze2.pdf ] as part of his STV method, which is intended to have vote management work only when to do otherwise would make the method fail Droop proportionality. I'm not completely sure if I've got it right, but I think it does it somewhat like DSV, by running vote managements for every voter so that manually doing a vote management confers no advantage.

I tend to favour counting exact proportionalities at national (=whole
election) level ((if one wants PR in the first place)).

One slight issue here is how to define proportionality.  It is implicitly
assumed that if a voter votes for a candidate, they also support the
candidate's party.  However, as can be seen with personal votes,
this is not always the case.

If candidates are seen as individuals then the "rounding errors" of such small units are typically higher than the "rounding errors" of big units like parties.

(What I was thinking was basically that if there is one quota of voters that have opinion X then the representative body could have one representative that has opinion X. This could apply to parties but also to smaller groupings and individuals as well as other criteria like regions (=> regional proportionality) (and even representation of other orthogonal groups like women, age groups, religions, races if we want to make the system more complex).)

This is the idea that I've based my "honest voter multiwinner comparison" program on. With a party-neutral voting system, proportionality of individuals make no sense since there's only one individual - the only way to make that work would be to have weighted power in the assembly. Therefore, what is important is proportionality of opinion, if we assume that voters prefer those with opinions similar to their own to those with opinions less similar to their own.

If you want to make it even more abstract, you could say: if there's a method to how voters rank (or rate) candidates, and this method ranks candidates according to proximity of some standard of information, then the assembly should be proportional with regard to that standard of information.

Party-neutral methods like STV use no inputs other than the ballots themselves, so those have to infer the proximity or proportionality directly. In a way, party list "cheats" (or goes beyond the assumptions) because it lets voters give their opinions (on one axis - the party membership axis) directly. One could also make a system that similarly "cheats" by knowing the location of every representative and voter, minimizing the average distance, for each voter, to the closest representative. I think that would be unwieldy, though, and there'd be the issue of weighting (how much better/worse is a close representative that disagrees with you than a faraway representative that agrees with you?).

The extreme would be a voting system where people just say how much they agree with an opinion, for all relevant opinions, and then the system picks the maximally representative assembly. Such a method is not desirable, I think, because it would be very vulnerable to strategy, and someone would have to say which opinions were "relevant" and then redo the list when voters' priorities change and other opinions become relevant. In a simulation, one can do this easily because the voters vote mechanically (and so the what the opinion "really is" doesn't matter), but in the real world, not so much.

Another option is to allow a voter vote for local candidates and then
as their last choice, vote for a national list.

This is maybe yet one step more complex since now candidates can belong to different orthogonal groupings (several local parties; one party covers all local regions). Or maybe you meant to allow voting only individuals locally, not to support all local candidates of all parties as a group.

The local count would be standard PR-STV, but with the same quota
nationwide (and a rule that you must reach the quota to get elected).

Ok. National level proportionality could influence the election of the last candidates in the districts.

Unallocated seats would then be assigned using d'Hondt or similar
method based on the amount of votes transferred to the national list.

Also, it could be in effect an open list.  The person elected would be
from the district that transferred the most votes to the party's national
list.

Maybe all districts would be guaranteed their fixed number of seats (typically based on the number of citizens of each district). The extra seats would be first allocated to parties and then to districts (using some appropriate algorithm).

That sounds like MMP. I think MMP can work if done right (with STV instead of FPTP as base, and reweighting to avoid lista civetta). Using party list here is probably better than the party-neutral version where you'd rank representatives for local, regional, and national levels, and then it keeps the reweighting at each stage; simply because there would be an immense number of candidates at the national level, and ranking them all would be Herculean.
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