Here's one explanation to why LNH might be more important to voters than monotonicity.
Most voters are used to election methods where they bullet vote one of the candidates. It is a quite natural thought that if one votes multiple candidates on a single ballot then the vote that the second favourite gets may take some power away from the first favourite. This may not be based on facts, but of course we don't expect the voters to be aware of all the technical properties of the methods. The voter may be happy and trust the experts if they tell that this particular method is LNH compatible and therefore they can mark also their later preferences without losing power. Also this may be based on facts but need not be. Strictly speaking it is enough if it is more probable that later preferences will help the voter than that they will cause harm. Therefore a method that is LNH compatible in 90% of the cases may be good enough, i.e. the voter could happily mark also the later preferences in the ballot. Monotonicity is a similar but reverse case. Typical voters expect their vote to support the candidates that they vote for. They don't expect it to make the results worse from their point of view. Therefore the voters are not afraid of non-monotonicity but are happy to vote although it could be that their vote will make the results worse. If the experts would convincingly tell the voters that their vote may actually lead to a worse result, then maybe some voters would stop voting in the hope of improving the results. But also here it can be claimed that it is enough if it is more probable that the vote will improve the results than it is to make them worse. Voters may thus find LNH more important than monotonicity. But this does not mean that the method should be formally LNH compatible. It is good enough if the methods typically behave as wanted. It is easier for experts to convince the voters if they themselves are convinced of their cause, e.g. as a result of a compatibility proof that proves that the method meets some criterion 100%. Sufficient compatibility with the criteria may thus often be enough. And risks may be higher in areas where the voters don't expect risks than in areas where they expect to find them. But the fact remains that voters may fear some threats more than others, rationally or irrationally. Juho --- On Sun, 21/12/08, James Gilmour <[email protected]> wrote: > > The reason I believe LNHarm is more valuable than > > monotonicity is that when a method fails LNHarm, the > voter is > > more likely to realize in what insincere way to vote > > differently, in order to compensate. When a method > fails > > monotonicity, a voter will rarely know to do anything > > differently because of it. > > LNH is important to ordinary electors, as I have explained > in a recent post, at least where the voting system is > susceptible to LNH > effects. If the vote counting method is not LNH-compliant, > electors are likely to vote strategically in an attempt to > avoid or > mitigate the effects of LNH-failure or to try to gain some > real or imagined advantage from its effects. > > Monotonicity, or more specifically, the lack of > monotonicity, is of no importance whatsoever in public > elections because neither > candidates nor voters can exploit it. It would be > "nice" if the vote counting system were monotonic, > but we cannot have > monotonicity AND some of the other criteria we consider > desirable. For example, monotonicity and later-no-harm are > incompatible in > IRV and STV-PR. Of the two, LNH is important - > non-monotonicity is irrelevant. > > James Gilmour > No virus found in this outgoing message. > Checked by AVG - http://www.avg.com > Version: 8.0.176 / Virus Database: 270.9.19/1857 - Release > Date: 19/12/2008 10:09 > > > ---- > Election-Methods mailing list - see > http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
