By Jameson Quinn, October 2015. [Last I checked, JQ was a grad student at Harvard. Slight editing by WD Smith which hopefully did not significantly alter anything JQ had to say. WDS is not necessarily endorsing any of JQ's claims or proposals here; he is merely re-posting them.]
Posted here (/CanadaSA2.html) just just to serve as a reference point for further discussion.
We shall regard voters as "female" and candidates as "male" just to make wording clearer.
1. Begin with a list of candidates, each of which is either independent or a member of a party, and each of which is also running in a single riding. Any party with 2 or fewer candidates is considered as a set of independent individuals. (This does not harm them in any concrete way.)
2. Each voter rates all the candidates in her riding on an 0-9 nuerical scale; and can additionally "write in" one candidate or party if she wishes. (Write-ins use a robust system to respect voter intent and avoid spoiled ballots insofar as possible.)
3. Each voter owns one "delegated point." If she names a candidate, it goes to that candidate. If she names a party, it is divided between all the candidates in that party, in proportion to how many points they got directly. Otherwise, it is divided equally between the candidates she top-rated.
4. Top average score in each riding wins. ("Scores" are totally separate from "delegated points.")
5. For each seat awarded so far, N/(S+1) points are removed, where capital N is the total number of points awarded (the number of voters who top-rated or wrote-in at least one candidate), and capital S is the total number of seats to be filled. These points are subtracted from the winning candidate himself. If more points are needed, they are taken in equal absolute numbers from all other same-party candidates who still own points. If all candidates in the party run out of points entirely, that party is regarded as eliminated, and no more points are removed for that seat.
6. If at any moment, the total points for all candidates of a given party exceeds n/(s+1), where lowercase n is the total number of points remaining, and lowercase s is the number of remaining seats, then the candidate in that party with the most points is elected. In that case, n/(s+1) points are used up, as above.
7. Whichever party has the fewest total points remaining is eliminated, and all candidates in that party may give their points to another non-eliminated party, or allow them to become exhausted. If they give them, then the points are divided between the candidates within that party in proportion to how many points they got directly. Points cannot be transferred between parties twice; they become exhausted when the second party they were held by is eliminated.
8. Awards and eliminations, as described in the last two paragraphs, proceed until all seats are awarded.
A. Almost all styles of voting which people are likely to try are at least reasonably close to strategically optimal.
B. Party gatekeepers have no role in voting, and the system in general gives little or no way for party members to reward/punish each other. This helps avoid the system devolving into corrupt "heavy whipping."
C. By the same token, the voters have the power to remove any unpopular candidate from office, even if that candidate has the support of their party colleagues.
D. Ridings are only a little bit larger than they are today, yet full proportionality can be achieved.
E. All voters have a local representative from their riding.
F. Voters can delegate to somebody they sympathize with ideologically, and the system is likely to use that vote for some candidate who is close to that ideology, insofar as possible.
G. Counting votes is simple and summable.