: Do the math…
RasmussenReports.com says Howard Dean leads in Iowa. The article adds:
At this point in the process, national polls are not as significant as individual state polls. As a practical matter, it is likely that Dean will continue to lead among all Democrats at least until the Iowa caucuses on January 19. The results in Iowa are almost certain to shake up the national poll numbers and could also have a significant impact on polling for the New Hampshire Primary.
The refusal to deal with the implications of the Mayer predictive model is just stunning.
It’s NOT about predicting the future. That’s foolishness for pundits. It’s about understanding how a terribly important system works.
I’m certainly no expert in probability, but let’s take an elementary look at it anyway. A campaign is a far more complex system than a coin flip. Yet to nail a coin flip nine out of ten times, the way Mayer has nailed 9 out of 10 campaigns, is a .59 probability.
Or, we might consider it this way: Not accounting for preferences (which is actually very important), you have a 1/x chance of choosing the correct candidate in any given election (1 is your choice and x is the number of possible choices). So the Mayer model achieves a probability that we might express at (1/x)9.
But the preferences as indicated in polls have an influence on your choice in a primary election (Re: Abramson et. al. 1992. “‘Sophisticated voting’ Voting in the 1988 Presidential Primaries.” American Political Science Review. 86:55-69.). In other words, citizens tend to back perceived “winners” because they don’t want to “throw away” their votes. Being a rhetoric scholar, I’ll leave it to the math jockeys (Jay Manifold, perhaps?) to figure out how this affects the probability. It is the matter of preference, and how it is constructed (by the press, I argue), that makes the model so important to consider.
The point of my inadequate little exercise is not to nail down the probability, or predict the future, but to establish that the results of the Mayer model are statistically significant and, therefore, are telling us something important about our system of choosing presidential candidates. When will journalists begin to listen? (via Political Wire)
From the Mayer data, we see that the model reaches a probability (Adjusted R2) of 77 percent:
Regression Equations for Predicting Primary Vote Shares
———————————————————
1980-1992 1980-1996 1980-2000
———————————————————
Regression Coefficients
National poll standings .94(.14) .99(.13) 1.05(.11)
Total funds raised .02(.08) .00(.07) -.02(.06)
Constant 1.31(3.37) 1.57(3.13) 1.72(2.66)
Adjusted R2 .69 .70 .77
Dependent variable = % of the total vote won by each
candidate in all primaries held by that candidate’s
party during the entire primary season.
Two independent variables = % of party identifiers who
supported each candidate in the last national Gallup
poll before the Iowa caucuses; and the total amount
of money each candidate raised before the election
year divided by the largest among of money raised
by any candidate in the party’s race.
———————————————————
UPDATE (3:10 p.m.): Jay Manifold responds (moved from the comments section):
This isn’t so much a math question as a behavioral one: how likely are people to fall into line with a perceived majority?
This paper (44 kB *.pdf) notes that “in 1992 while 11.1% of Clinton supporters and 17.3% of Bush supporters actually defected from their preferred candidates, 31.8% of Perot supporters switched their votes to a major party candidate. The defection rate of Perot supporters was even higher in 1996 …. while 15% of Clinton supporters and 10% of Dole supporters switched their votes, 48.5% of Perot supporters deserted their originally preferred candidate.”
Presumably it’s easier to “defect” during primaries. Suppose half of primary voters are trying to pick the winning horse. There are 9 choices, and a heavily-publicized poll reveals that the top 4 are supported by 24%, 20%, 11%, and 10%, respectively, leaving only 35% to be divided up among the other 5, for ~7% apiece.
If half the votes are, in fact, going to the perceived leader(s), that field of 9 is going to narrow very quickly, largely irrespective of the individual campaigns’ finances, and it is not going to be that hard to guess the final winner. Indeed, your chances of guessing correctly are more like 1/2 than 1/9.
But for the Mayer model to work 9 out of 10 times, it has to work a whole lot better than the flip of a coin. You correctly note that the likelihood of 9 heads in a row is less than 0.2%. Well, the ninth root of .9 is nearly 99%, which may crudely represent how well the Mayer model works at any given election.
This suggests, as has been mentioned in this space before, additional effects which cause the nomination process — across numerous states and including non-elected delegates — to statistically converge on the candidate leading in national polls. One such effect is the “sophisticated voting” you mention; I surmise that another is the readiness of appointed delegates to line up behind a perceived winner.
The only thing I can think of that could seriously throw this off is determinedly ethnic or geographical intra-party voting patterns, neither of which seem especially likely. I find the possibility of sectional voting at the general election worrying, but that’s a whole ‘nother can of worms.
This isn’t so much a math question as a behavioral one: how likely are people to fall into line with a perceived majority?
This paper (44 kB *.pdf) notes that “in 1992 while 11.1% of Clinton supporters and 17.3% of Bush supporters actually defected from their preferred candidates, 31.8% of Perot supporters switched their votes to a major party candidate. The defection rate of Perot supporters was even higher in 1996 …. while 15% of Clinton supporters and 10% of Dole supporters switched their votes, 48.5% of Perot supporters deserted their originally preferred candidate.”
Presumably it’s easier to “defect” during primaries. Suppose half of primary voters are trying to pick the winning horse. There are 9 choices, and a heavily-publicized poll reveals that the top 4 are supported by 24%, 20%, 11%, and 10%, respectively, leaving only 35% to be divided up among the other 5, for ~7% apiece.
If half the votes are, in fact, going to the perceived leader(s), that field of 9 is going to narrow very quickly, largely irrespective of the individual campaigns’ finances, and it is not going to be that hard to guess the final winner. Indeed, your chances of guessing correctly are more like 1/2 than 1/9.
But for the Mayer model to work 9 out of 10 times, it has to work a whole lot better than the flip of a coin. You correctly note that the likelihood of 9 heads in a row is less than 0.2%. Well, the ninth root of .9 is nearly 99%, which may crudely represent how well the Mayer model works at any given election.
This suggests, as has been mentioned in this space before, additional effects which cause the nomination process — across numerous states and including non-elected delegates — to statistically converge on the candidate leading in national polls. One such effect is the “sophisticated voting” you mention; I surmise that another is the readiness of appointed delegates to line up behind a perceived winner.
The only thing I can think of that could seriously throw this off is determinedly ethnic or geographical intra-party voting patterns, neither of which seem especially likely. I find the possibility of sectional voting at the general election worrying, but that’s a whole ‘nother can of worms.