Which voting error is less awful?

Politics & Elections
1

It’s two weeks before the election, and you’re head of your state’s Board of Elections (or equivalent body). Given the chaos of, well, everything, you’ve assigned me to come up with a protocol to defend democracy in your state.

At last, I come to you with two plans for protecting the sanctity of democracy. We have time to implement either of these plans, but there’s no time to come up with a third plan: if we don’t adopt one of these two plans, there’s guaranteed chaos. When you see the plans I offer, you might decide to fire my incompetent ass, but you’ll either choose one of them, or you’ll go down in history as the worst Board of Elections Boss the nation’s ever seen.

PLAN 1: This plan cuts way down on errors (including both incorrectly-cast ballots and incorrectly-denied ballots): they’ll only comprise 0.2% of all ballots cast. However, those errors will overwhelmingly affect one of the two major political parties: almost all the errors will consist of preventing that party’s votes from being registered.

PLAN 2: This plan has far more errors: as many as 1% of ballots will be incorrectly-cast, and as many as 1% of voters will be incorrectly turned away. However, these errors will be spread equally among the two political parties.

Plan 1 prevents a lot of fraud and turns very few people away, in other words, but its errors are much likelier to affect the outcome of a tight election. Plan 2 allows significantly more fraud and turns significantly more people away incorrectly, but is much less likely to affect the outcome of a tight election.

(Plan 3–doing anything else–could create anywhere between 2 and 10% of ballots being incorrectly cast, and we don’t know whether one party will be more affected than the other.)

So which plan do you choose?

My theory is that conservatives will tend toward plan 1, and liberals will tend toward plan 2, and that there’s some underlying difference in values there that might be worth exploring; but I’m not sure. If all you want to do is accuse the other party of being a bunch of cynical hypocrites, while I might agree with you, can you not do that here?

2

Even though it might get me tagged as a conservative, my risk-averse personality compels me to go with the option that produces fewer errors: Plan 1.

3

That’s really interesting to me. To me, being risk-averse means going with option 2.

There are two risks:
Plan 1: overturning the correct results of an election
Plan 2: denying people the right to vote, or incorrectly giving people the right to vote. (I know these are technically two different risks, but I’m lumping them together for comparison; if that’s an unfair lumping, well, I’ll take my lumps).

I consider plan 1’s risk much worse than plan 2’s risk.

4

In which mathematical discipline is a total error rate of .002 worse than .01?

5

You’ve left out the units. I always tell my students, don’t leave off the units!

Your units is “individual votes.”

In which mathematical discipline is a total error rate of 0 worse than 1?

The units there are “elections.”

6

If it’s biased (rate of errors fror one party’s ballots is higher for the other).

7

Will people be informed about the consequences of each of these plans, and will they believe what they are told? If yes, I think Plan 2 is the only possible choice. Better to have everybody more or less equally pissed off than to hold an election that is manifestly skewed in one party’s favor.

If not, I believe Plan 2 is still the right thing to do, so I’d still go with it, but it’s going to degenerate into a nasty clusterfuck of fraud-and-unfairness accusations on all sides that will result in democracy being considerably the worse for wear, so it’s a tougher call.

8

I don’t tend to think of tight races as any kind of default, so on the whole, I consider “individual votes” a more reasonable priority to shoot for, particularly given that the ultimate goal is preserving the “sanctity of democracy.”

9

Keep in mind that it’s statewide: there will be literally thousands of elections affected, from district water manager up through president. The presidential election may not be tight, but there will almost certainly be some local elections somewhere that are tight.

10

Okay, but the way I parse that, the potential is there for Plan 2 to achieve 1% compromised outcomes split into two tranches of 0.5%, vs. 0.2% with Plan 1.*

I really hope I’m misunderstanding something here.

*(for the set comprising tight races)

11

I want to know more (which is kind of fighting the hypothetical). most specifically, the nature of the errors of the plans. Are they new errors (or types of errors)? Are they the same errors we’d make if we did nothing - just fewer of them? What’s the cost/time of fixing either plan (I understand that it can’t be done, but I want to know a few more details of why not)? Can it be fixed in a future election cycle or is doing the plan going to entrench the error over time?
Also, and probably most important, how close do elections tend to be in my jurisdiction or do I expect them to be this time around? If I expect the overwhelming majority of the contests to be blowouts, I might be more inclined to plan 1; if I expect the overwhelming majority to be very close races, I might opt for plan 2 - because I’m not changing the outcome, but I am impacting more individual voters.

Either way, I’m getting out in front of this and saying “We’re making a change to the current system that brings down the number of incorrectly cast votes from X to Y and incorrectly turned away voters from W to Z.” to keep the story between no-plan and a plan, rather than between two plans.

12

I’m pretty sure you are, because you’re not catching the way errors would shake out.

Let’s say an election with 10,000 votes will be decided by 10 votes, 5,005 R to 4,995 D.

Under plan 1, 20 votes will be miscast, overwhelmingly in the same direction. That’s enough to shift the election, if the shift is R–> D. The final outcome would be something like 4,987 R to 5,013 D.

Under plan 2, 100 votes will be miscast, but they’ll be spread equally. 50 R votes turn D, and 50 D votes turn R. The outcome stays substantially the same.

13

Okay, that makes sense.

14

Plan 2 does less harm.

15

1% of voters incorrectly turned away vs a wrong 0.2% swing
Even in the very tightest of elections a 0.2% margin would be extraordinarily rare.

I’d have to go for the plan that disenfranchises the least amount of people

16

Disclaimers of course, I make no claim to understand any math beyond basic arithmetic.

That being said, Plan 2 does less harm on the average. There is no guarantee that it will not affect individual races. There is no way a model can be assured of equally disqualifying votes every time. That would require that every other flip of the coin is heads and all other flips are tails. If that was possible you could make a model where the only elections that were not perfectly legitimate were ones where the margin is one vote.

So across several election cycles Plan 2 might be more fair, but each individual election would most likely be better served by Plan 1. Submitted as final answer, now explain to me like I am eight years old why I am wrong. (Seriously – I think very slowly and have a hard time recalling all relevant data.)

(The part I am going to say that I should just skip and remain quiet – but hey my father is dead and he will never know I did not follow his edict: “Temporary, keep your mouth shut and let others assume you are dumb rather than speaking and removing the doubt.”) In a far, far down ballot race where only Five-Hundred votes are cast, you are still unlikely to run into a circumstance where Plan 1 would not give you good results – and further, if it is that close THAT PARTICULAR race should trigger more investigation. Either a re-count or a runoff election, so I also claim false dichotomy.

And I say all that even have read all those brain development and brain chemistry books that convincingly argued that common sense is almost always wrong.

17

Agree.

18

This reminds me of the joke about the three statisticians hunting ducks. One shoots a foot high, the second shoots a foot low, the third puts down his shotgun and proclaims “We got him!”.

Errors have to be random (or we need to rename them for starters). Random occurrences do not happen every other try. Flipping coins will usually average out, but it is not unusual to have fairly long anomalies along the way. Seven same flips in a row being a common amount of “streaks”. Taking that as fact, if you flip a coin ten times you should end up with five heads and five tails but if a streak of seven happens – or two smaller streaks of four, the results are badly skewed. Over a hundred flips things should even out but I doubt every time someone flips coins one hundred times it comes out fifty/fifty. And obviously a thousand flips should be even more accurate.

So when counting ballots, the last ten ballots are always a group of ten. If you say that using Plan 2 everything has worked perfectly to the model during an election of One-Thousand votes even (1,000.0) – after Nine-Hundred Ninety votes, you could have an anomaly of seven in a row favoring one candidate or party and skewing the results.

Now on the next election of roughly a thousand votes it could skew the other way and the model would be correct over several election cycles. But accuracy will almost always be a better option in real world application.

The example you give in the post I quote above, your point only holds true if real life perfectly mimicked the mathematical model. I am saying there is no possible way to be assured of that in real life over a sample of one. A sample of one for those last 100 votes could be 40 vs 60 or possibly even 39 vs 61. It would only be over several elections that things would average out.

And now it is time for the better educated to show me my errors. Feel free to be kind about it if it is not too much to ask.

19

Yes, but since tens of thousands of elections have been held going back a couple hundred years, close ones are not unheard of. Naturally, there’s a wiki-list of them:

The first 20 or so are all tied elections.

20

The larger the number of voters, the better plan B is. No, the errors won’t exactly cancel out (well, probably not). And the net number of swung votes (votes swung one way minus votes swung the other way) will increase, with increasing numbers of voters. But on average, it’ll only grow as about the square root of the number of voters, so the more voters, the smaller a proportion the swing will be.

So there’s a threshold number of voters where the two plans are equally bad, and above which A is worse and below which B is worse. But with the numbers given, that threshold number is going to be in the double digits. Which is far smaller than the constituency for any governmental election in the US. So in the real world, A will always be the worse plan.