SPACE voting is a summable proportional, optionally-delegated voting method for nonpartisan elections such as a city council. Essentially, it works as partially-delegated STV.
Voters are asked to choose one candidate and to optionally grade the rest either "acceptable" or "reject".
If they choose exactly one candidate, and do not grade any others, their vote is delegated; that is, converted to an STV ballot using the public, pre-declared endorsements of their chosen candidate, and the results of the initial tally.
Before the election, each candidate has the opportunity to endorse other candidates. If a candidate chooses to endorse, they must endorse at least two other candidates.
A vote for a candidate is converted to an STV ballot by adding those endorsed by that candidate in the order of their initial vote tallies. So if X endorsed W, Y, and Z, and if the direct votes for these three were 800, 1000, and 600 respectively, a delegated vote for X would be converted to X>Y>W>Z (that is, X first, Y second, W third, and Z fourth).
If they choose exactly one candidate, and grade any others, their vote is undelegated; that is, converted to an STV ballot using the tally of voters who chose the same candidate. Say that of the 1000 votes for X, there are 700 which accept Y, 500 which accept Z, 400 which accept W, and 100 which accept V. 700+500+400+100=1700 approvals, which is greater than the total number of votes involved by 700, so there are 700 excess approvals. 100 filled-in ballots which include all 4 secondary candidates would account for 300 excess approvals, leaving 400; 200 more filled-in ballots which include 3 candidates would account for the remaining 400 excess approvals. So we have: 100: X>VWYZ (divide equally among remaining candidates) 200: X>WYZ (ditto) 700-300=400: X>Y 500-300=200: X>Z 400-300=100: X>W
Total filled in: 100+200+400+200+100=1000.
Once delegated ballots are filled in, an STV (single transferrable vote) counting process proceeds as normal.
Optional rule for discouraging vote-funneling
If a candidate X gets less than 1/3 of a quota, and does not endorse at least 2 other candidates who get more than 1/2 of a quota, then X's delegated votes will not be transferred until all candidates with less than 1/2 of a quota of votes have been eliminated. During the time between when X is eliminated and when their delegated votes are transferred, their delegated votes count as exhausted for the purposes of calculating the quota. Thus, during that time, the quota for other candidates is slightly lower.
This reduces the ability of minor candidates to reliably funnel votes to a specific major candidate. Minor candidates can still be useful to a broader coalition, but have a harder time giving an unfair advantage to a single major candidate.
This rule does not unfairly punish voters who choose a minor candidate, since their votes are still eventually transferred.
PLACE voting: a similar system, for replacing FPTP in a partisan context (such as nationwide or state/provincial elections in Canada, US, or UK).
GOLD voting: An older, slightly more complex version of PLACE.
OL/D voting: similar to GOLD, but without the constraint of one candidate per riding, and with a slightly weaker elimination rule.
PACE voting: a non-summable version of SPACE; more complex for voters, but simpler in terms of vote-counting.
Proportional 3RD voting: an old version of PACE.