Thursday, April 23, 2009
Technical notes on dropping
Now, for some thoughts on whether the system we have is a good vote-counting system. Perhaps you wonder how it is that dropping a losing candidate can get you another Senator, and understanding this may change how you view this "manipulation."
Dropping a candidate before counting starts has two impacts. The first is that quota is decreased. The second is that the votes for that candidate get redistributed earlier than they would otherwise.
The quota concept is a bit weird, which is why when votes get redistributed matters. After a candidate's votes are redistributed, the voting algorithm checks if any candidates are over quota. If they are, those people who have voted for that candidate have a portion of their votes (the portion not needed for quota) redistributed to their next choices. Any future votes that would be redistributed to that candidate are instead redistributed to the next candidate in line on that ballot.
What makes this weird is that this means that those only those whose vote was associated with the candidate when she reached quota are counted towards that quota and partially redistributed. Any future votes that would be associated are not counted towards that quota and fully redistributed. This means you'd rather have those voters who only support one of your popular candidates associated with that candidate early, and those voters who support one of your popular candidates and a bunch of your other ones associated late, so that their full vote redistributes.
Dropping a candidate reduces quota and lets other candidates reach quota earlier. Depending on the order of votes, this can make the distinction between partially redistributed votes and fully redistributed votes work in your favor, and it will typically benefit the party which has more total votes, because they have more votes to rearrange.
A fair case can be made that the partial/full redistribution distinction is silly. An alternative, for instance, could hold that additional voters associated with a candidate who reached quota will only be partially redistributed, and the redistribution of the previous votes associated with that candidate would be slightly further redistributed. This system has its own drawbacks, one if which may well be that the result can be changed by rounding errors. But it's something to think about. It won't necessarily make it impossible to change results by dropping candidates, but may prevent some of it.
. . .
. . .