All else is never equal

Andrew's short note about someone's hypothetical Trump victory scenario prompted this post.

The concocted scenario is: "Had 45,000 gone the other way in Arizona, Georgia and Wisconsin, Donald Trump would still be president." This sounds like a reasonable hypothesis. The analyst took the three states that Trump lost by the smallest margins, and flipped them.

But such an analysis is flawed. The flaw is the unspoken assumption of "all else being equal". Said differently, the assumption is that those 45,000 voters represent an independent bloc of voters - their voting propensities are perfectly aligned with each other, and yet perfectly uncorrelated with other voters.

As Andrew explained, if 45,000 more votes had gone to Trump, this would have suggested a shift in national swing towards Trump: the voting margins in many other states would also have shifted away from Biden. The state-wide voting margins are themselves correlated, so an all-else-equal condition is unrealistic.

If those 45,000 voters in Arizona, Georgia and Wisconsin made a different decision, many more voters in other states probably also would have changed their votes!

Andrew then did a first-order approximation of this correlation. His model assumes that the 45,000 extra voters in those three states embodied a purely national trend so that the same percentage swing occurred in every state. Under this condition, we'd expect about half a million more votes for Trump nationally, rather than just 45,000.

(Note: Because of the strange electoral vote system we have in the States, we'd need to see a national swing of 500,000 votes so as to find 45,000 extra Trump votes in those three states, which would be necessary to flip the electoral votes of those states, thus flipping the election.)

Of course, the first-order approximation is too simplistic. The correlation of state voting margin to the national voting margin depends on whether a state is red, blue, or purple, on turnout, and other factors. One can build more sophisticated models but the principle is still the same: different parts of the system are correlated, and so manipulating one part almost definitely causes other parts to change.

***

All-else-equal assumptions are extremely popular.

In sports commentary, for example, one often hears arguments, such as if the star 3-point shooter on the team had scored the average number of baskets, then his or her team would have wiped out the deficit and turned the loss to a win. However, if that player had played better, the whole team would likely have played better, the other team might have adjusted their tactics, etc. If more of that player's shots have gone in, s/he might have attempted more (or fewer) shots.

Businesspeople like all-else-equal assumptions too. Consider an online retailer who currently charges customers to return merchandise. What happens if the return fee is eliminated? We'd expect the frequency of returns to jump, costing the retailer a bundle.

But that's not the only behavior that may change. The retailer might enjoy an increase in sales as some customers previously didn't make purchases because they disliked the return fee. Another jump in sales could result from customers buying different sizes or styles of the same item, with the intention of retaining just one. These effects may apply across all merchandise and regions or they may be restricted to certain product categories or regions.

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On a second look, the Trump re-election hypothesis requires some further assumptions about voter behavior. Biden's total vote margin in those three states was just under 45,000, according to Wikipedia. If voters flipped their votes from Biden to Trump, it would only require half of those voters to bridge the gap. Thus, the concocted scenario is one in which 45,000 additional Trump voters showed up to even up the margin. In addition, the scenario requires that no additional Biden voters appeared. Or, it requires that a net 45,000 additional votes for Trump materialized.

Ironically, illegal measures to rig the election break these correlations. If one were to just stuff the ballot boxes with 45,000 additional Trump votes, then it would be possible to close the gap without seeing other voting margins shift.

Comments

[Michael Droy]

"Ironically, illegal measures to rig the election break these correlations. If one were to just stuff the ballot boxes with 45,000 additional Trump votes, then it would be possible to close the gap without seeing other voting margins shift."

Well of course. And the flip side (the real point) is that 45,000 stuffed votes for Biden might well have won him the election. Which is why the investigations (and cover ups) into vote rigging in 2020 were so important.

There is a peculiarity about US elections that few non-Americans are aware of. There are 3009 counties which count votes - 158m vote in 2020. The county votes are added up at the State level

Now to me in Britain (or to anyone in Europe), that means an average of 53k a county. Stuffing 45k votes then becomes a real challenge. Hard to stuff more than 5% in a single county or it would be obvious. 45k votes would be about 18 times 2500 votes. How do persuade the staff at 18 different counties to do that? Without anyone telling tales?

But to an American this is easy to explain.
https://en.wikipedia.org/wiki/2020_United_States_presidential_election_in_Arizona#Results_by_county

Arizona - 15 counties, 3.4m votes, with a staggering 2,076k in one County - Maricopa (of which you may have heard had some controversies).
Could Dems have stuffed the 45k votes in Maricopa? Of 100k votes, let alone the 11k the Dems won by? Well easily.

Georgia. 159 counties, 5.0m votes - about 30k per county? Dems won by 12K How can that be fixed? Well Fulton county had 524k voters and was one of 4 counties with 370k+ votes.

Wisconsin 71 counties, 3.3m votes, about 47k a county, But Milwaukee had 459k votes. Easy to stuff the 20k votes that Dems won by.

For non-Americans like me, the hard part to understand is why whole cities are treated as one reporting unit (sometimes whole, sometimes split into 2 or 3 parts). And then we need to know that the big city/counties are all controlled by local Democrat authorities. That is true in Republican states too. (Hence the claims that Dems couldn't vote stuff in Repubican run states were always deception).

So the real issue with the story is not that 45k votes could not get stuffed - but that vote stuffing has only been feasible for Dems city authorities. Republicans control all the small counties with 20k-50k voters.

45k votes - 3 strongly Dem controlled counties totalling 3m voters - an easy fix.

I think I know the response. This is mad Trumpism because the very idea that Dems might have fixed the vote cannot be discussed and so on.