Strategy

Scenario #5 (following the logic of #2): If we support 1 candidate, are neutral to 2 others, and are strongly against the remaining 7, we should vote for the one that we support and, amongst the two whom we are neutral to, the one who has a higher chance to win. Again, the objective is to minimize the chance of those we are against.

Is there any scenario that we should cast only one vote? Let's consider this:

Scenario #6: We support 1 candidate and are strongly against the remaining 9.

Yes, in theory, we should only vote for the one whom we support and leave the other vote blank.

However, in real life situation, it is almost always possible to, amongst the 9 whom we dislike, find one that is least repugnant. Even if there is none, there may well be other social reasons that you would like to vote for one of the abominable nine - for example, one of them is your classmate or old friend. In this case, your spare vote serves a social rather than political function.