Not really sure how to explain this other than with examples. Judging from the way the ballot is counted, a voting system appears to “assume” something about the voter that may not be warranted. This fact can help explain some of the system’s flaws.
- C1 (FPTP) assumes/acts like you only like one candidate, and all others are equally bad.
- IRV assumes that you have a clear favorite, and then you prefer your second choice slightly above your third, and so on. It is like a limit of a geometric series of utility: 1, ε, ε2, … as ε → 0.
- The flaw of IRV not electing consensus winners is contained in this one, as IRV assumes any choice but your first is nearly tied with everything else.
- Borda assumes that your preferences of the candidates are equally spaced. That is, you lose as much utility from going from 1st to 2nd as you do from going from 6th to 7th.
- Condorcet assumes (paradoxically) that you value all “I prefer X over Y” relations as equally strong. (Which is actually contradictory, as if you think X>Y>Z, your preference for X over Z is clearly stronger than X>Y or Y>Z.)
- Approval Voting assumes you value the candidates in exactly 2 tiers and have no opinion on candidate pairs within a tier.
- Score Voting assumes that you… um… oh yeah: that you are not going to want to exaggerate if candidates drop out.
- STAR Voting is like Score but it then assumes you will want to (or will not, if you give both the same score) exaggerate once the leading two are decided.
- 3-2-1 Voting is like Approval, but with 3 tiers. (The rest of the system is more about assumptions about the “best winner” than the voters themselves. This one has another flaw, like Borda and some of the various Condorcet cycle rules: it feels like the system, rather than the voters, chose the winner.)
I think the only voting system that makes no assumptions would be that weird one on the Kialo discussion where your vote is
if <boolean expression on candidates>: <score vote> elif <second boolean expression>: <possibly different score vote> <...>
(Actually… never mind, that one assumes your internal preferences are representable as numbers and you do not believe any cycles X>Y>Z≥X.)