"Later-no-harm" may seem desireable to an individual voter considering his/her own favorite extreme candidate. However, the same voter would probably want the converse for one's polar opposition. Therefore, "later-no-harm" may be a two edged sword. Whether one values it depends on whether one wants divergeance toward polarization or convergence toward compromise.
As an alternative to satisfying "later-no-harm", a method may level the field for all voters by disallowing ties and truncation (demanding a complete or whole ranking). Jrfisher 12:40, 17 Aug 2005 (PDT)
I'm afraid I don't understand your argument about polarization as opposed to convergence. The point of LNHarm, in my opinion, is that voters may feel free to offer their compromise choices without having to worry that this will cause a preferred choice to lose.
In my opinion, disallowing truncation doesn't eliminate the problem that Later-no-harm addresses. It's just that now you don't rank a candidate instead of not ranking him, you rank a candidate higher as opposed to randomly. Kevin Venzke 15:03, 17 Aug 2005 (PDT)
Divergeance / Polarization
By discouraging voters from (or rewarding voters for not) voting among their disapproved candidates, we would leave each faction's favorites to be sorted by the factions themselves. This sorting by a subset of the electorate (mimicking what happens in American primaries today) will tend to elevate an extremist within each faction (set of clones), and the dominant faction's extremist will likely win overall.
I call this divergeance because a change in balance between factions would swing the election to an "opposite" extreme without swinging through the "middle". Therefore, a system that "protects" against compromise choices will be biased toward office holders who represent factions rather than whole districts. In the limit case, voters bullet vote, and we are de facto right back to first-place plurality.
Granted, disallowing truncation (and tie voting) does not eliminate LNH, but it does apply the effect to all voters so we can then work with methods that solve other, more important problems. Jrfisher 09:28, 18 Aug 2005 (PDT)
Can you give a hypothetical example? Later-no-harm only "protects against compromise choices" when a higher-ranked candidate could have won instead. When a method does not "protect against compromise choices," then voters have incentive not to rank those choices. So a method that satisfies Later-no-harm should be more likely to elect a compromise candidate, since the voters don't have truncation incentive.
What problem do you consider more important than obtaining full rankings? Kevin Venzke 11:29, 18 Aug 2005 (PDT)
By the way, there are three main reasons why I stopped worrying about Later-no-harm:
1. It seems to be incompatible with the Minimal Defense criterion.
2. Even MMPO retains some approval elements. You may be able to rank A as well as A>B, but it could well be that the only way to elect one of these candidates is to vote A=B.
3. Although MMPO satisfies LNHarm, it is still strategically unwise to vote for the worse frontrunner, since if it's expected that you'll do this, the worse frontrunner's supporters can use burying strategy against you to steal the win.
According to the favorite betrayal write-up, Condorcet methods (except Kevin's) violate it. Given what I know and like about Condorcet methods, this suggests that there's something wrong with either that criterion or its application. Jrfisher 09:28, 18 Aug 2005 (PDT)
So "given what [you] know and like about Condorcet methods," they can't fail a criterion unless something is wrong with that criterion? What about the other criteria that Condorcet is incompatible with?
If you disallow ties in the ranking, it is quite clear that Condorcet methods fail FBC. Assume that these votes are sincere:
Assuming this is a Condorcet method, then regardless of which candidate is elected above, some voters have incentive to insincerely rank a candidate strictly above their favorite candidate.
The danger of this is that if voters realize that sometimes they need to rank a viable compromise above their favorite, they may be cautious and do this all the time.
My Condorcet method (ICA) satisfies FBC because it is tweaked to do so. It doesn't strictly satisfy the Condorcet criterion. Here is an example: