Moving averages

In a previous post here, I mentioned moving averages:

In a first-past-the-post election, a moving average can be applied to this result in order to eliminate fast fluctuations.

This raises two questions:

1. What sort of moving average, and how should it be applied?
2. Why is a moving average not necessary with proportional representation?

For voting, the best moving average is a simple moving average. This means the data points aren't weighted - that is, the voting result for any given day is just as important as the voting result for any other day. Applying this involves simply choosing a number of days to include in the moving average. The result is to smooth out rapid fluctuations in voting results.

Another, even simpler, method is to announce results for a first-past-the-post district less often than every day. Results could be announced weekly or monthly, for example. There is an important balance to be considered, however: longer reporting periods smooth out fluctuations when they happen to occur, but they also reduce the immediate accountability of the representative.

Elections using some form of proportional representation requires no smoothing or extended reporting periods because any fluctuation would have to be at least as large as the number of votes needed to secure a seat in order to have any effect. Such a large change is by definition significant. This holds true whether the election uses party-list proportional representation (like the European elections) or the Additional Member System (like Welsh and Scottish elections).

Fluctuation in a first-past-the-post district is, in itself, an important indicator. It occurs when:

1. The electorate is highly polarised. That is, the two leading parties have nearly the same number of votes.
2. Neither party is able to gain and hold the support of the swing voters in the district.
3. Those swing voters do not abandon the two leading parties for a third party, but instead continually switch their votes between the two leading parties.

Knowing that fluctuation is occurring in a district should act as a major motivating factor not only for the two leading parties but for all other parties with candidates in that district.