So, I’ve been discussing this idea of allowing voters to score the candidates in pairs, such that you could give a 100% margin to A>B and B>C simultaneously. In essence, it’s Condorcet but each matchup is done based on Score voting.
The main conundrum for this is to decide how its transitivity rules should operate. Suppose a voter gives a 30% margin to A>B (meaning they might have, for example, scored A 80% and B 50% in the A vs B matchup) and a 40% margin to B>C. Obviously, transitivity means they must give a positive margin to A>C i.e. they must score A higher than C in the A vs C matchup. But, since we’re talking about ratings, we also have to take into account how much higher A should be scored relative to C. The two ways I see are:
- Take the strongest margin in all of the matchups transitively next to each other, and make this the minimal margin to be used for the next matchup in the chain.
** This means giving at least a 40% margin to A>C.
- Add up all of the margins in the matchups transitively next to each other, and make either this or 100% be the minimal margin, whichever is smaller. (This is Score voting’s version of transitivity).
** In this case, this means giving at least a 70% margin to A>C.
Either of these transitivity rules gives the same result in Condorcet, because if a voter gives 1 vote to A>B and does not vote B below C, then they’ll automatically give 100% support (1 vote) to A>C as well.
The Score voting-based transitivity rule is more restrictive (i.e. if you score A>B 50% and B>C 50%, then you have to give A>C 100% based on Score’s transitivity but only at least 50% in the other transitivity rule), but I suspect it might be the more logical rule.