The only way to write a substantial book is to lock yourself into a particular ideology, stop second guessing, and just work.

Accordingly, an author’s first words since their last major publication are those they have denied themselves. They are nearly sacred in their innocence, and with the urgency to be spoken ahead of every other thought left unexpressed.

So after 4 years writing her tour de force ode to community participation, it is refreshing but not shocking to read Nadia’s newest post on democratic abstinence.

It’s puzzling however, that Nadia ends by writing:
“The reason I’m curious about this topic is because the idea of not voting seems to provoke a sort of digust [sic] and moral outrage that, say, democratic lotteries or liquid democracy, does not, even though these are arguably equally radical proposals.”

The gigantic difference between abstention, lottery and liquidity is that only the first is at all attainable. If I meet someone who wants to implement an alternative voting scheme, no matter how radical, my reaction is not disgust or horror, it’s “good luck.”

Voting reform is famously slow, practically so because it tends to involve constitutional amendments, and theoretically so because every politician who could implement it has already benefited from the existing system.

In contrast, abstaining is something that anyone can do right now. In fact, it’s the default position if you simply decide to not do anything at all. It generates moral outrage because it’s an actual threat, not just a radical idea.

Perhaps something should take the place of politics as a better meaning-making structure, but I don’t have a good idea of how abstaining gets us there, or what change it provokes that qualifies it as a “civic engagement strategy”.

US voter turnout is already very low compared to other wealthy countries, and our elections are very close, and the logistics, somewhat questionable. If the idea is to further delegitimize the American presidency, it is difficult to understand how we could try any harder, or accomplish any more.

There are currently 245 million eligible voters in the US, what if cut that down to 10,000?

What if we conducted this process completely at random?

My tongue-in-cheek defense is that US Presidential Elections are currently decided by just 538 voters in the Electoral College, so this would represent nearly a 20x increase in suffrage.

More seriously, here are 4 arguments in favor of the 10,000 random voter scheme.

1. It’s unlikely to return different results
The easiest criticism of the 10,000 Voter proposal is that it leaves too much to chance.

Let’s do some quick simulations.

Assume there are 10,000 voters with the same preferences as 2016, 46.1% for one candidate, and 48.2% for the other. What are the odds of accidentally electing the less popular candidate?

odds = 48.2 / (46.1 + 48.2)
trials = 1000
voter_counts = [10**2, 10**3,10**4,10**5,10**6]
for voter_count in voter_counts:
  wins = 0
  for trial in range(trials):
    wins += sum([
      1 if random.random() < odds else 0
      for i in range(voter_count)
    ]) > voter_count/2.0
  print(wins)

The results are:

Of course, this depends on margins, but 46.1% to 48.2% is already a very close race. With just 10,000 voters, you have around a 98% of elections choosing the candidate with the most supporters.

In comparison, our current system has only elected the candidate who wins the popular vote in 53 out of 58 elections, or 91% of the time.

2. Save 57 million hours
A report on the 2016 election found that “the median and average times spent at polling locations are 14 and 19 minutes, respectively”. Since there were 136.7 million votes cast, that means 43.3 million hours spent voting.

That doesn’t even include commuting. Another paper found “the average residential parcel has a distance of .356 mile to its polling place”, so it’s more like a 6 minute round trip, plus 19 minutes in line, for a cost of 57 million hours.

3. Reduce racial disparities
Even more disturbingly, the same paper finds that:

…a 1-standard deviation (.245 mile) increase in distance to the polling place reduces the number of ballots cast by 2% to 5%

Additionally, the first report highlights racial disparities in waiting times, stating:

…relative to entirely-white neighborhoods, residents of entirely-black neighborhoods waited 29% longer to vote.

At a very rough estimate, that corresponds to an additional 5.5 minutes. Which is around .9 miles at a residential speed of 10mph, or around 3.7 standard deviations of distance to polling place, for a drop of around 6%-15%. Again, this is extremely rough, it may not scale linearly.

Even ballparking these figures, it suffices to say that seemingly minor logistical issues can impose a tremendous cost.

4. Voters are motivated to take their privilege seriously
In 1789, the US was a democracy, but only to a privileged few. Though states differed, suffrage was generally limited to white male landowners who comprised a mere 6% of the population. At the time, the US population was around 4 million, so the voting class comprised a mere 240,000 people.

Of that 6%, only 20% actually made it to the polls (others had appointed electors), leading to a country of 4 million electing John Adams in 1796 with a mere 35,726 votes.

It’s easy to imagine how those lucky enough to vote might be endowed with a sense of responsibility, privilege, and even pride.

In contrast, voting as one of over 100 million people today, I feel helpless. Even if you’re lucky enough to live in a swing state, Andrew Gelman puts your odds of influencing the election at just 1 in 10 million.

This results in extremely low voter turnout, but also in an unwillingness to take one’s privilege seriously, and invest time in a deep understanding of the issues at stake.

Imagine instead that you were chosen as 1 of just 10,000 voters across the entire country. Your odds of influencing the election would skyrocket, and motivated by a sense of deep privilege, it’s difficult to imagine casting that vote as automatically as many voters to under the current system.

Instead of a despondent morass, we would get 10,000 Americans imbued with the responsibility to represent their country.

Before you cringe, I am not, as a random blogger, claiming to have resolved a 70-year-old Nobel-prize-winning dilemma.

Instead, the answer comes from Eric Pacuit who wrote Stanford Encyclopedia of Philosophy’s excellent summary of Voting Methods and Wesley H. Holiday, a professor at Berkeley.

Before we get into the solution, a brief introduction to the problem itself. If you’re familiar, jump to the page break.

Michael Nielsen once wrote: “You are almost certainly better off reading deeply in the ten most important papers of a research field than you are skimming the top five hundred.”

In voting and in social choice theory more generally, Arrow’s original paper certainly qualifies. It is approachable, clearly argued, and from one of the greatest economists of the last century at his absolute best.

But if you really don’t have time, the brief summary is: it is formally impossible to produce a voting system (of a certain class) that satisfies 3 basic criteria, including Independence of Irrelevant Alternatives. As Arrow states: “the choice made by society from any given set of alternatives should be independent of the very existence of alternatives outside the given set.”

This seems obvious, but is totally violated by many common voting systems. In Plurality Voting, a “spoiler” candidate is one who has no chance of winning, but alters the results for other candidates. Consider a close race between a Democrat and Republican “spoiled” when votes are diverted to a Green Party or Libertarian candidate.

IIA is also violated by Ranked Choice Voting implemented by Borda Count (candidates get points according to their rank). The voter preferences:

• 40% prefer Alice, Carol, Bob
• 60% prefer Bob, Alice, Carol

Are spoiled by Carol. Without her, Alice gets (4 _ 2 + 6 _ 1 = 14 points) while Bob gets (6 _ 2 + 4 _ 1 = 16 points). With Carol’s inclusion, Alice still gets 14 points, but Bob falls to (6 * 2 = 12) points and loses the election.

There are voting systems that satisfy IAA, but are either outside the class Arrow describes, or violate other criteria.

As Arrow’s proof is formal and flawless, the solution is not a new system that somehow escapes its claims, but rather, an argument that convincingly dissolves it’s assumptions.

In their recent pre-print Axioms for Defeat in Democratic Elections, Holliday and Pacuit leverage another seminal paradox in social choice, that of circularity. In Condorcet’s Paradox, aggregations of linear preferences result in circular preferences, sometimes leading to instability: i.e. a winner is declared even though more than 50% of voters would prefer switching to an alternative.

In the top example, it’s clear that A defeats B, and the inclusion of C makes no difference; however, in the second, the introduction of C changes our intuitions about the relationship of A to B. If we have the same n for all ballots, it is not at all clear that A should defeat B, or in fact, who the winner should be at all!

So the introduction of a new candidate, without affecting voters’ relative rankings for existing candidates, convincingly and justifiable changes the aggregate rankings.

In a more extreme case, our intuitions might actually flip. Without C, we have:

• 6 prefer A, B
• 4 prefer B, A

Which is a clear win for A. But with the introduction of C, the first 6 voters split, and we get:

• 3 prefer: A, B, C
• 3 prefer C, A, B
• 4 prefer: B, C, A

In this second case, A beats B on 6 ballots, B beats C on 7 ballots, and C beats A on 7 ballots, so B appears to be dominant.

This is the same logic we used above to demonstrate a flaw in Borda Count, but with the renewed intuition that it’s a sensible result, rather than an “unfair” spoiler.

The authors go on to propose Coherent IIA as an amendment. Another recent preprint of theirs introduces Split Cycle Voting which escapes the revised Impossibility Theorem, and is also Condorcet consistent.

I haven’t finished a thorough read of both papers yet, but was excited about this particular result, and eager to share it.