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Vaniver comments on Werewolf, Cambridge UK Less Wrong Meetup April 1st 2012 - Less Wrong
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That reasoning sounds like a bias against inactivity to me. The comparison is between being down 1 villager for sure, or being down {2 villagers, 1 villager 1 werewolf}. That has to be justified on the grounds that killing a werewolf gets you more than killing a villager costs you. Consider your first game, and assume that the players have no information the first round (i.e. you have a day before a night). Lynching someone at random gives them a 1/6th chance of winning, and a 5/6th chance of being at 3 villagers and 1 werewolf day 2; not lynching someone at random puts them at 4 villagers and 1 werewolf day 2. Whether or not that's a good idea depends on the relative chances of villagers winning with 4 villagers and 3 villagers against 1 werewolf. (If villagers have p(win)=.5 with 4, and anything more than p(win)=.4 with 3, then they should go for the random kill. The worse the villager's chances, the more they should be winning to kill randoms- assuming there's only one werewolf.)
If the village never lynches, the game is closed on werewolf victory.
There's also a social dynamic at play. Particularly in larger games, the village tends to split into factions. The wolf wants to encourage this, but doesn't want one faction to defeat the other too quickly. So the wolf wants to plausibly switch sides frequently. When there's no lynch, switching sides has less consequence. The more decisions with consequence that must be made, the more lies the werewolf must tell and more inconsistencies the wolf must reveal.
Sure. I expect it's a solid strategy for the villagers to lynch if there's any evidence to single someone out, and possibly even in the absence of such evidence (I can't model tells and suspicion well enough to do the relevant math). But that needs to be grounded in "we're better off lynching than not," not "we have to do something!" There are probably scenarios where inactivity is a better option.
If the wolf or wolves can form a nucleus for that something and there are no other credible options, inactivity is better. The wolves also vote as a secret bloc - if they're good, they can determine the outcome of a "do something" vote (although if they're not as good as the village, this reveals them pretty severely).
(This is my experience with the game, not a worked solution or anything.)
If a majority of players agree that a random player needs to be lynched, this is possible. Everyone picks a number from 1 to N, where N is the number of living players, and you add the numbers mod N and then lynch the corresponding player. This is robust against colluding wolves: even if exactly one person picks a random number, the sum will be random.
Of course, I don't see this strategy being adopted, because it arguably takes the fun out of playing.
I explicitly prevent my players from introducing 'true' sources of randomness like coin flips ('true randomness' in that all parties can see and agree it was random), or from recording information with pen and paper. The key to challenging and enjoyable mafia is embracing the 'social reality' concept: no fact or claim can be free from ulterior motives, no truth can be clearly untwisted.
I guess then the challenge of randomization is whether players can do modular arithmetic with large primes in their head.
The additional factor one has to take into account is the odds of gaining information, and the likely effect of that information gain upon improving your chances of killing werewolves at future lynchings.