Thursday, May 05, 2011

"Making your vote count" and "wasted votes"

These phrases are commonly heard, but infrequently explained in a coherent and meaningful manner. It is very unlikely that a single person's vote will ever really make a difference in a large election, and of course this is entirely appropriate for a democracy where we all (supposedly) share equally in voting power.

However, people still vote, and other people try to work out whether it is rational or not (see Andrew Gelman's blog for lots on this, search for the text "rational to vote").

One point that I don't think I've seen made, is that people might reasonably think their vote "counted" if it either increased or decreased the winning margin. The margin of victory should affect the behaviour of the electee, as they will be more willing to take a hard-line position and alienate (some) voters in a safer seat, and more eager to please those on the fringes in a marginal one. Any change in the number of people voting for either the 1st or 2nd placed candidate will alter the winning margin, so the (a priori) marginal value of each of these voters is non-zero.

Conversely, a vote placed for the 3rd or lower party really is worthless, as the marginal effect of more or fewer votes here is zero, at least until they overtake the 2nd party. The winner might even prefer to see a strong 3rd place candidate, in the hope that they could threaten to cannibalise the support for the 2nd place.

Maybe this is one reason why I think that AV would be beneficial, as it guarantees that a majority - and in practice usually a large majority - of the electorate will get to see their vote "count" in this manner. In simple majority voting (first past the post is such a stupid name I can't bring myself to use it) it is still likely that a clear majority of voters will see their votes count (I expect this usually happens in all seats), but in practice it will often not be such a large majority, and in many cases this will only happen if people are willing to vote tactically (and know who to vote tactically for, which isn't necessarily obvious a priori).

4 comments:

William T said...

If you really do want all votes to count (equally) then you can't go past proportional voting - all votes DO count the same in respect of proportion of representation in the parliament (except for very fringe parties that don't get over the threshold if there is one).

For your standard FPP or AV/STV system however, votes for smaller parties are always discriminated against. For instance in the last UK election conservative votes were worth 3 times as much as Liberal votes in terms of seats won. It's even worse for smaller parties - the 285,000 green voters end up with a single MP whereas Conservative voters get an MP for every 35,000 of them.

It's even worse for AV - in the last Australian election the greens got 11% of the votes and one MP. And that MP got less of the first preferences than the next candidate - the only reason he won was that most of the libreal voters put him above Labor for their preference vote...

James Annan said...

AV has one big advantage of being an incremental change that is highly compatible with the present system. A fully proportional system sounds nice in some ways, but I don't see what the fundamental justification is for stopping at the level of representation in *parliament*. If you care about proportionality uber alles, surely the *Govt* should have a proportional representation of all parties...

William T said...

If you care about proportionality uber alles

Well, no, I didn't say that - you're shifting the goalposts AND raising a straw man...

In any case, yes I would expect that if the largest party only got 35-40% of the votes, then the will set up a coalition to get above the 50% line. And yes, then the government can claim to represent a plurality of voters...

David B. Benson said...

Arrow's (Voting System) Theorem