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.
Say that your preference is A>BC; that A, B, and C have all endorsed each other and nobody else; and that D has endorsed C and E. Should you vote for your true favorite A, or compromise by voting for C? If you do the latter, you may cause C's tally to pass E's, so that C gets D's delegated votes before E does. So a favorite betrayal strategy may work in this case.
However, if A has any chance of winning, then it's unlikely this strategy makes a difference, because there are likely enough votes from A for C to win a seat without needing D's votes. So the only time this strategy is really worth it is if the cost, in terms of reduced chances of electing A, is negligible anyway.
In theory, it could in some cases be strategic to vote for a candidate you did not like at all and then accept several candidates you did like. If the first candidate you voted for was eliminated, your vote could carry along a fraction of an extra vote to the candidates you did like. However, the risk would be that your vote would go to a candidate you did not like. In general, this is not likely to be a viable strategy.
In particular, this strategy could only steal a fraction of the non-delegated votes for a weak candidate — likely a negligible amount. And it would always reduce the initial tally for your true favorite, which could have downsides in various ways.
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.