You can convey this by only submitting a single choice on your ballot (a powerful tactic in AV). Conversely, you can vote everyone BUT the one you wish to harm. And by default you can vote NOTA. While it may be that Approval Voting is not the "perfect" answer, it is far better than most and comes with the added benefit of easy adoption/implementation and simple explanation.
Yeah, but then you run the risk of a Trump getting elected in an election between Trump, Hillary, and Bernie, where you really want Bernie, and you really don't like Hillary at all, but you'll still take her any day over the utter disaster that is Trump.
This is why AV isn't that great: all they have to do is put up a truly revolting candidate to scare voters into voting for the not-as-revolting candidate, and she gets elected because there's no way for voters to express a clear preference.
tl;dr for non-experts (I co-founded the Center for Election Science and have studied voting methods since 2006).
The idea behind LNH is that if I vote for the Green in 1st place, it's "safe" to then rank the Democrat 2nd, because that can't cause the Democrat to defeat the Green. See this explained visually in this video by Andy Jennings, another CES co-founder who did his math PhD thesis on voting methods.
http://www.youtube.com/watch?v=JtKAScORevQ
The Later-no-harm criterion is highly misleading, because "safe" here means safe for the CANDIDATE. But tactical voting is about what's good for the VOTER, not the candidate. With IRV, the Green voter's best strategy is to actually rank the Democrat in 1st place. So the whole notion that he can safely rank the Democrat #2 after he's ranked the Green #1 starts with a false premise. If he's rational, he WILL NOT rank the Green #1. It's the same reasoning that Democratic primary voters have about far left candidates. Even if you win the nomination and advance to the general, you're so far left that you'll probably lose against the Republican, by not capturing enough of the center of the electorate.
Approval Voting actually makes it safe to ALWAYS vote your favorite. And, in general, to vote for everyone you prefer to your favorite of the frontrunners.
From what I've seen of most Condorcet methods, the best way to tactically vote differs if there is or is not a Condorcet winner, and often become a major mistake in the other circumstance.
Basically it means unless you know what the results will be tactical voting will have a rather good chance of backfiring on you, making it not worthwhile, which seems like a good thing to me.
This is the "expressiveness fallacy". https://www.electionscience.org/library/expressiveness-in-ap...
tl;dr
Total information throughput for a voting system is a function of THREE things:
1. Amount of information you can express on a ballot.
2. Accuracy of that information (which is distorted if the system gives you an incentive to dishonestly/tactically vote) .
3. Tabulation efficiency — how effectively does the system utilize the info on the ballots (for example there are numerous ranked voting systems from IRV, to Borda, to the entire Condorcet family; and IRV is extremely lossy) .
When you factor these all together, Approval Voting does surprisingly well, especially because it's so good at #2 and #3. See this graph of performance as measured by Bayesian regret. http://scorevoting.net/BayRegsFig.html
Essentially what's happening is that the people who's approval threshold sits between candidates A and B (i.e. those people who only approve one of them) will, in a statistical sense, have about the same A-vs-B preference as the people who voted for both or neither of them. So the aggregate effect doesn't really suffer from your inability to express a ranked preference for all candidates. Voting is statistical.
To really drive that home, note that you could switch to a better voting method and STOP VOTING, and STILL get better election outcomes. The tiny impact your vote has on the process is statistically negligible. The properties of the voting system matter vastly more.
Also in the messy human emotional sense, it's still _unsatisfying_ that I might Approval vote for Bernie and Hillary but I still want to say I like one better, and I still think that difference matters.
As you know, there are various other methods (Condorcet, STAR, 3-2-1, etc.) that keep most of approval's advantages, but sacrifice simplicity for better expressiveness. It would be as unreasonable for the advocates of such methods to try to undermine real-world campaigns for approval, as it would be for approval advocates to undermine those other methods.
Can you show how the differences in outcomes is better using the Condorcet method?
The IRV page extrapolates the majority principle for two choices to more than two choices, but its not obvious that this is correct. There are arguments that need to be made before we can start comparing the quality of outcomes between voting methods.