Here is a simple example of why misreporting of past votes affects the apparent "defection percentages." Of course, someone who is looking to evade the lesson of this example can complain that it isn't "realistic." That's true. It isn't designed to be realistic: it is designed to be simple.
Suppose we have information on 20 voters: whom they actually voted for in 2000 and 2004, and whom they
say in 2004 that they voted for in 2000. In this simple example, a single Gore voter (#10) says that s/he voted for Bush. #10 also votes for Bush in 2004. Otherwise, one Gore voter votes for Bush in 2004, and one Bush (2000) voter votes for Kerry, a wash.
actual 2004 report actual
voter 2000 vote of 2000 vote 2004 vote
1 Gore Gore Kerry
2 Gore Gore Kerry
3 Gore Gore Kerry
4 Gore Gore Kerry
5 Gore Gore Kerry
6 Gore Gore Kerry
7 Gore Gore Kerry
8 Gore Gore Kerry
9 Gore Gore *Bush
10 Gore *Bush *Bush
11 Bush Bush Bush
12 Bush Bush Bush
13 Bush Bush Bush
14 Bush Bush Bush
15 Bush Bush Bush
16 Bush Bush Bush
17 Bush Bush Bush
18 Bush Bush Bush
19 Bush Bush Bush
20 Bush Bush *Kerry
So, we have 10 Gore voters and 10 Bush (2000) voters; 9
reported Gore voters and 11
reported Bush (2000) voters; 9 Kerry voters and 11 Bush (2004) voters.
If we make a table based on
actual vote in 2000, it will look something like this:
2000 vote (%) Kerry % Bush %
Gore (50%) 80% 20%
Bush (50%) 10% 90%
(The "defection" percentages are 2/10 = 20% for Gore-to-Bush and 1/10 = 10% for Bush-to-Kerry.)
But if we make a table based on
reported vote in 2000, it will look something like this:
2000 vote (%) Kerry % Bush %
Gore (45%) 89% 11%
Bush (55%) 9% 91%
(The defection percentages are 1/9 = 11% for "Gore"-to-Bush and 1/11 = 9% for "Bush"-to-Kerry.)
So, in this simple example, the effects of overstating having voted for Bush are (1) to exaggerate the apparent share of Bush (2000) voters in the 2004 electorate, and (2) to understate the difference in defection rates between Gore voters and Bush voters.
Is this example too simple? Of course it is. That's why I wrote an entire paper exploring the quantitative dynamics, as well as presenting the empirical evidence for misreporting of past votes. The response?
*crickets*