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I am thinking about this particular form of proportional representation for a parliamentary system and I am wondering if it has been used before. This is how it works.

Half the seats in Parliament are filled by first past the post vote, similar to what is being used in the UK and the US.

Then, a list is made for the losers of each party by the order of how close they are to the winner of their districts.

Now, say a party got 40 seats in the first half of the Parliament but it should've gotten 80 seats based on popular vote across the country. Then, the party got 40 seats extra. However, these seats are not chosen by the party like the open list in Germany or the closed list in Venezuela but are taken from the first 40 names on the list of losers for each party.

So each party is proportionally represented.

The reason I like this method is that for example if a winner in a district gets 35% of the vote while the 2nd placer and 3rd placer got 33% and 20% of the vote, respectively. Then, there is a strong chance that one of the losers will get a seat, thus about 60% of the district's vote is represented.

The only disadvantage I can think of is that some districts will get more than one representative while others will get only one.

Has this form of election system been used before and what are the pros and cons of such a system?

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I would say that one con of this system is that you are using a vote for a specific candidate as an indicator of support for the party as a whole.

It is quite plausible that a voter may vote for a candidate of party A in his or her district even though the voter generally prefers party B. For example, the party B candidate in that district may have been part of a scandal.

I'm not sure that the method for selecting losing candidates to fill the extra seats is fair. A key factor is the number of candidates competing in the district. If only two candidates are competing, then it is easier for losing candidates to get a higher percentage of the vote. If many candidates are competing, then losing candidates are more likely to have a lower percentage.

Are you familiar with the single transferable vote? It is used by several countries and gives a very fair way of allowing more voters in a district to be represented by one of the winners of that district.

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    This is more akin to the kind of system offered in Germany: mixed member proportional representation. There, compensatory seats are given to parties who are underrepresented in the geographic districts. Those seats are based on a list of people written by party leaders. Note also that in the system proposed here, the compensatory picks are chosen by losing margin rather than percentage of the vote.
    – Brythan
    Commented Aug 20, 2017 at 21:52
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    @Brythan, I missed the part about losing margin being used to select the losing candidates. Doing it that way, you could potentially have 10 candidates elected from one district if they all were close in votes. Seems that you need to take into account magnitude as well as margin. Reminds me of a paper I wrote some years ago: jstor.org/stable/27698107
    – minou
    Commented Aug 20, 2017 at 22:59

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