A recent state legislature election in Virginia piqued my interest because it featured a candidate rematch of a contest that I featured in the first post of this blog almost two years ago because of its interesting mathematical implications. That 2017 House of Delegates vote ended in a tie, and it was resolved months later literally by drawing lots.
The stakes of this ancient form of a dice roll were magnified because the party control of the Virginia House of Delegates hung in the balance. The final tally ended differently in the November 2019 rematch, and in that story are some interesting lessons on mathematics and voting. So, how did it turn out, and what has changed since 2017?
The math of the 2017 vote
In 2017, the final court-approved vote count for the seat contested by Democrat Shelly Simonds and Republican David Yancey was a tie, resulting in the aforementioned drawing of lots. This action awarded the race, and control of the legislative body, to the Republicans. Two years later Simonds won the rematch with about 58% of the vote, a substantial majority, and the Democrats will take control over the House of Delegates in January, 2020.
I considered two mathematical questions in that 2017 tied race. First, even in a race of that size, additional recounts would likely have resulted in vote tallies different from the “official” one. Indeed, the first count had Simonds at ten votes behind. A second tally then put her one vote ahead before the third tally showed a tie. We place great importance on vote counts, and most of the time we get the totals “close enough” that the true winner is well within a comfortable probability spread, but there literally may be no such thing as “an exact vote tally” in many of our most-contested elections. And yet we certify these elections anyway, often with great consequence, even though there is no definitive winner.
The second mathematical question was raised by the determining an election outcome via drawing lots, or some other method designed to physically simulate randomness (also called an aleatory process, which literally means “dice throw”). The drawing of lots has had mystical “God’s will” connotations for more than 2000 years, even in the early Christian church.  The ancient Greeks used the method to talk about fate. The mathematics of probabilistic randomness using similar processes underlies our many public lotteries (a word itself derived from “lots”). Finally, an alternative explanation is determinism, a more scientific form of fate. 
In any event, it has been a tumultuous two years in the Virginia legislature on issues such as Medicaid expansion, gun control and voting rights with a Democratic governor and a Republican House of Delegates. Life would likely have been quite different for many Virginia citizens had the lots in the bowl arranged themselves only slightly differently. The more one thinks about that 50-50 outcome probability, the less defensible governance by this method becomes.
Changing “political restaurants”
Especially because the two candidates in this race were the same people in both elections, the other interesting mathematical story here is the shift of significant numbers of voters from one candidate to the other. One direct cause of the percentage change in this particular race was the court-ordered “un-gerrymandering” of Virginia legislative districts. The court had ruled that Republicans had consciously and illegally “packed” minority voters into as few districts as possible, and the new legislative boundaries put more Democrats into the district that Yancey had won in 2017.
However, in both the 2018 and 2019 November elections, it has been clear that shifts are much more organic than simply explainable by changing district lines. In a series of posts last year I wrote about the concept of Markov chains as a way to conceptualize how Republicans had radically changed their stances on several traditional policy positions over a brief period of time around the 2016 election.  Markov chains can be thought of as watching the progress of people either remaining loyal to a particular restaurant over time or “defecting” to a competitor’s restaurant. The idea is that a certain percentage of people “switch sides” individually and incrementally over time, and changing rates of loyalty versus rates of defection, have interesting effects down the road, as illustrated by restaurants “A” and “B” below:
Depending on the relative sizes of the two loyalty rates and two defection rates shown above, it is difficult to predict the outcome of this “dynamic system” without some computer-aided simulation as to whether one of these restaurants will “crash,” or whether a new “steady-state” level of business for each will emerge for each. At some point, it is most likely that a smaller number of customers at, say, restaurant B will mean a smaller number of defections, even if the rate states the same, at which time the loyalty rates and defections in the other direction will offset further losses, resulting in a new “equilibrium” between the two restaurants. Without some continual “goosing” of the rates, the effects will eventually peter out.
The simple version of that
Markov chain math is really just a way of saying that people change their minds on restaurants and social attitudes one person at a time, and usually without fanfare. We are all influenced by a wide variety of social structures, neighbors, religion, and social media. For instance, one way to look at the social shift toward greater acceptance of same-sex marriage is as one person at a time becoming aware of an LGBTQ family member or acquaintance who does not “fit” the dominant negative social stereotypes, with a higher rate of people quietly “switching sides” in favor of broader social acceptance than the rate of people “defecting” in the other direction. The issue did not “go away,” rather a new “steady state” emerged where, at least for the time being, outright opposition to same-sex marriage has been effectively muted.
In the political version of this, my suggestion here is simply that a slightly higher rate of people are individually “defecting,” deciding, often against social pressure from their peer groups, that Donald Trump’s daily Twitter-based challenge to societal and political norms is no longer worth supporting. At the same time, there remains a “defection” rate for those newly in favor of Trump’s “pro wrestling/reality TV” model of politics, but currently this rate appears small by comparison.
As the Markov model suggests, the process is dynamic. The clues to the future are most likely found in tiny rates of change to individual, one-at-a-time perception. Political scientists, pollsters, demographers, and pundits, mostly partisan themselves, often claim Gnostic-like “secret knowledge” as to why people switch sides. However, we humans are often not honest, even to ourselves, as to why we quietly “change restaurants.”
Markov chain analysis minimizes the “Why?” question in favor of asking “How many?” My current bet is that the rate of moves away from Trump fealty exceeds his “new convert” rate. If I am wrong, God help the nation. There are times when there is big change in one defection rate or another, but that is usually not required. Slow and steady often wins the race in Markov terms.
The Democratic Primary “restaurants”
The Markov chain concept can be extended to multiple “restaurants,” although this gets difficult to picture when there becomes an exponentially expanding set of loyalty and defection rates as more candidates enter the field. And one of the biggest “restaurants” currently out there is named “Undecided,” with its own defection and loyalty rates.
While the Iowa February caucus system has its share of critics, I found my past participation in the Democratic Party version of this event to be a fascinating study of Markov chains in action. After a year of having political candidates show up for coffee gatherings in even the smallest Iowa towns, you gather in a large room with your literal neighbors and “choose a restaurant” by standing in a group representing your candidate. If any groups comprise fewer than 15% of the total number of attendees, those people have to “choose another restaurant” after some time set aside of discussions and coaxing. This process continues until all less-than-15% groups are gone. Defection rates and loyalty rates get played out in real time.
Note that this could well be a messy process this year with so many candidates, and with so few candidates currently above that 15% threshold. As the British say, Iowans are “spoilt for choice.” The candidates with the highest loyalty rates and lowest defection rates will gain representation to each county convention, where the winnowing continues, and hopefully eventual representation at the national Democratic convention.
Real democracy can be a messy, hard-to-predict thing. We often forget that our Founding Fathers were themselves mostly elites (and obviously all males) who intentionally placed significant limits on pluralistic democracy, for example the original method for selecting members of the U. S. Senate and the entire mess of the Electoral College. The unintended consequences of that “original sin” first gave us only two viable political parties at any one time (a lesson most third-party advocates have yet to figure out) and more recently gave us Donald Trump.
In the meantime, think about why people keep coming back to some restaurants in your community, while other establishments fade away. Some candidates have enticed me for a one-time visit, but it gets harder for them to draw me back for seconds.
The 1998 film Sliding Doors, featuring Gwyneth Paltrow, is a clever story about the effect of “What ifs?” and 50-50 odds.
- Lots were drawn to select a thirteenth Christian apostle when one was chosen to replace the disgraced Judas Iscariot (see Acts 1:26).
- “Hard determinism” suggests that the initial state of the process and, say, the physics of the bouncing numbered balls in a lottery cage, determine the exact ball chosen. In other words, the process is only pseudo-random, or “random enough,” but the outcome is, as are all apparently-probabilistic outcomes, foreordained from time of the Big Bang. This position says that the events happening right now, at “time t”, are completely determined by the exact state of the universe the instant before now, “time t-1”.
- The shifts I documented at that time included past conservative support for moral probity from elected officials, for free trade, for small-d democratic institutions such as NATO, and for law-enforcement institutions such the FBI and the CIA. All of these have virtually flipped 180 degrees in a short period of time.