[sjfidsfkds]

If I approve of two candidates, but I like one more than the other, approval voting doesn’t seem to allow me to express that preference. Do I vote for both candidates, or only the one I like the most? As a naive voter who isn’t going to research that question, will I make the right choice?

[elihu]

It's a hard question. I think it comes down to: are you more afraid of your top choice losing, or your least-favorite choice winning? If the former, then just vote for your first choice. If the latter, vote for everyone but your first choice. (This is an improvement over FPTP because you at least have the option to support multiple candidates if you want to.)

Some people don't like this aspect of approval voting, and really want to give an ordering or a score.

Score voting is like approval voting, but you give a score. All the scores are totaled up, and the winner has the highest total. This is a pretty good system, but it has a problem: honest voters who aren't enthusiastic about a candidate might rate their candidate 6/10, whereas a very opinionated partisan voter might rate their candidate 10/10. So, the people with the most extreme opinions have more influence: 6 partisans gives a score of 60, whereas ten unenthusiastic voters also gives an equal score of 60.

Under score voting, strategic voting means always maximizing your positions: always 10/10 or 0/10, nothing in-between. Basically this is the same as approval voting. So, I'd suggest that approval voting is usually better because it puts strategic voters and honest voters on an equal playing field.

There's another voting system called STAR (score then automatic runoff), in which you use score voting to select the top two candidates, and then you do an instant runoff by maximizing all the votes for the top two candidates. For instance, if our top two candidates are A and B and if someone marked candidate A as 7 and candidate B as 4, then that turns into A:10 and B:0. If another person has A as 6 and B as 6, then they don't have a preference and that ballot is dropped.

STAR isn't perfect (what if an extreme party runs two ideologically-similar candidates and they both make it to the runoff?) but it's a pretty reasonable compromise system that allows voters to score candidates rather than just making a yes/no choice.

[juped]

you approve anyone who you approve of

approval voting is a special case of score voting where the range of scores is limited to 0 and 1. if you want to express different levels of preference, you can expand this range and get full score voting. the downside is this puts a heavier burden on the voter to decide on scores (if it's 0-99, i give my first choice 99, but what do i give my second choice? 98? 75? 50? my choice might depend on what i expect other voters to think makes sense as a score)