What level of PR do different systems get?



  • I think this is a question which does not get talked about enough. The obvious reason is that there are many definitions of PR and no single definition applies to all systems. However..... there is a somewhat meta concept of PR which one can apply across systems since I would not say they are really in conflict. No system can have no PR at all but partisan PR systems can arguably have full PR. I made this plot to try to get the conversation rolling.

    PRspectrum.JPG

    Disclaimers:

    • This is likely not to scale though I did my best
    • All multimember systems are 5 member
    • I put the two touchpoints of passing a quota rule and exact partisan PR. If there were more I would add them
    • The sequence of the multimember systems around the quota rule point is based on the Winner set stability definition of PR. Other definitions will give different sequences. For example I think SPAV is the only system of them which passes Proportional Justified Representation but that is not super commonly used since STV fails it.
    • These are just the systems which came to mind. I am likely missing a few important ones.


  • Without knowing Keith had made the chart above, I also made a chart to try and hone in on this concept.

    That said, I think graphing systems on a chart like this will always get pushback unless it's made with real data, and even then I doubt it's worth sharing...

    In any case, single winner elections which elect plurality winners will always have lower PR than those which ensure at least majority support, and methods which take into account voters secondary and tertiary preferences and level of support for other methods will also have a higher level of PR.

    Can anyone think of some better multi-winner methods that would qualify as semi-proportional?

    How proportional is a voting method? .jpg

    It's worth noting that an electoral system with no PR is possible (dictatorship) and perfect proportionality is also possible if a given election had everyone neatly assigned to a viable sized team, but I focused my chart on the actionable and democratic section of the spectrum.



  • I don't know that partisan PR is more PR than non-partisan PR. It's just less clear what exactly is getting portioned out.



  • @SaraWolk said in What level of PR do different systems get?:

    multi-winner methods that would qualify as semi-proportional?

    What do you mean by "better"? What about SNTV?

    @SaraWolk said in What level of PR do different systems get?:

    I don't know that partisan PR is more PR than non-partisan PR. It's just less clear what exactly is getting portioned out.

    If everybody votes along party lines then partisan systems are have higher PR than 5 winner systems because they elect the whole parliament at once instead of just 5. The resolution of a system is the number of winners in a riding. Although, many such systems put in limits of needing 5%.

    @SaraWolk said in What level of PR do different systems get?:

    It's worth noting that an electoral system with no PR is possible (dictatorship)

    Well sort of. That dictator will a least represent themselves so there is a tiny amount of PR.

    It would be interesting to try to simulate this. We would have to make a bunch of assumptions and choose a way to map candidate endorsement to party endorsement in a realistic way. But if we did have such a simulation we could then calculate an average Gallagher index for each system.

    @SaraWolk I am surprised you put Single Member STAR so far from Cumulative voting. I would think they would be much closer. But without a simulation I only have intuition to go on.



  • @Keith
    For "better" semi-proportional methods for inclusion in a chart I mean methods in use or that people are familiar with. Or methods that are too fabulous to not include. What's SNTV?

    Re Party List vs. nonpartisan PR, the difference there is the number of winners, not the partisanship.

    I have no idea where exactly STAR or Cumulative should go, or which order they would go in. I'd like to think they should be reversed, but I also have no basis for that.



  • @SaraWolk said in What level of PR do different systems get?:

    What's SNTV?

    https://electowiki.org/wiki/Single_non-transferable_vote

    @SaraWolk said in What level of PR do different systems get?:

    Re Party List vs. nonpartisan PR, the difference there is the number of winners, not the partisanship.

    Granted but if you partisan vote then the same ballot works for any number of winners. Parliaments are typically over 100 seats. You are never going to run a ballot with candidates for so many seats. So what I am saying is true in practice but not necessarily in theory.

    @SaraWolk said in What level of PR do different systems get?:

    I have no idea where exactly STAR or Cumulative should go, or which order they would go in. I'd like to think they should be reversed, but I also have no basis for that.

    I do not have the time to write simulation code. If only there were universities who would sponsor people to study this.


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