The Bias of 1-D Opinion Polling: Explaining the Low Polling Numbers for Candidate Beto O’Rourke

by | Sep 29, 2019 | Math Learning

In Electoral Opinion Sampling, whether of candidates, policies, or values, it is commonplace to ask subjects yes/no questions, where someone either choses one person out of a list of candidates or says whether or not he or she agrees or disagrees with a political statement. Such a question though only has one layer of information and disregards the unique nature of an opinion, which includes not only the final choice – voting for a candidate or policy – but also the reasoning behind the choice, the “why?” behind the claim. Thus, only the surface of the opinion manifold is measured through the yes/no questions of mass politics. This creates a bias in our statistical understanding of the population’s political views since it collapses the distribution of opinions into a single norm, leaving us with the impression of polarization, where people are either on the right or left of an issue with little sense of the commonalities or overlaps. Thus, when the political sphere appears polarized, it is more of a problem in measurement, than in the actual underlying viewpoints. To resolve this social-political problem of polarization, where the nation can’t seem to come to a common viewpoint, we must look at the depth of the opinion manifold by mapping out a system of opinions rather than a single norm.

We can use Game Theory to represent an opinion as an ordering of preferences, i.e. A < B < C < D < E < F. Where each choice-element of the preference set must be strictly ordered in relationship to each other, leaving a ranked list of choices, one has a strict ordering of preferences. This was used to represent opinion in Arrow’s Theorem of Social Choice. Yet, without any allowable ambiguity, the result proves an equivalence between the aggregate social choice methods of dictatorship (one person chooses the social good) and democracy (the majority chooses the social good). This explains the critical political observation that mass politics – based upon superficial opinions – often becomes fascist – where one personality dominates the national opinion at the exclusion of immigrant or marginal groups. This game-theoretic error of restricting preferences is equivalent to the recently noted behavioral-economic error of excluding irrationalities (i.e. risk-aversion) from micro utility-maximization. Instead, we can represent opinion as a partial ordering of preferences, rather than a strict ordering. Thus, an opinion is represented as a tree graph, algebraically by A >> B, B >> D, B >> E, A >> C, & C >> F, or a tree data structure, formatted as {A: (B: (D,E), C: (F))} (i.e. JSON). The relationship of inclusion (>>, i.e. A >> B) can be interpreted as ‘A is preferred over B’ or ‘B is the reason for A,’ depending on whether one is looking at the incomplete ranking of choices or the irrationality of certain value-claims. In micro-economics, this yields a non-linear hyperbolic functional relationship between individual opinion and the aggregate social choice, rather than a reductionist linear functional relationship. In a hyperbolic space, we can represent each opinion-tree as a hyper-dimensional point (via a Kernel Density Estimation) and perform commonplace statistical tools, such as linear-regression or the multi-dimensional Principal Component Analysis, resulting in hyper-lines of best-fit that describe the depth of the aggregate social choice.

This method of deep-opinion analysis is particularly useful for understanding electoral dynamics still in flux, as with the Democratic Primaries, where there are too many candidates for people to have a strictly ranked preference of them all. In such an indeterminate thermodynamic system (such as a particle moving randomly along a line of preferences), there is an element of complexity due to the inherent stochastic ‘noise’ as people debate over each candidate, change their minds, but ultimately come to deeper rationalities for their opinions through the national communication mediums. Instead of trying to reduce this ‘noise’ to one Primary Candidate choice so early in the democratic process when the policies of the party are still being figured out – similar to waiting to measure a hot quantum system (i.e. collapsing the wave-function of the particle’s position) while it is still cooling into equilibrium – we can instead represent the probabilistic complexity of the preference distributions. In preference orderings of democratic candidates, this means that while the underlying rationality of an opinion (deep levels of a tree) may not change much during an election cycle, with small amounts of new information the surface of the top candidate choice may change frequently. In order to make a more predictive electoral-political models, we should thereby measure what is invariant (i.e. deep-structure), always missed in asking people for their top or strictly-ranked preferences. While a single candidate may consistently be people’s second choice, he or she could end up still polling at 0%. If this ordering isn’t strict, i.e. always less than the top choice but above most others, then the likelihood of this ‘2nd-place candidate’ being close to 0% is even higher. Without the false assumption of deterministic processes, it is not true that the surface measurement of the percent of the population willing to vote for a candidate is equivalent to the normative rationality of that candidate – the 0% candidate may actually represent public views very well although such cannot be expressed in the 1-dimensional polling surveys. Thus, while the actual electoral voting does collapse the chaotic system of public opinion into a single choice aggregated over the electoral-college, such measurement reduction is insignificant so early in a democratic process with fluctuating conditions. As a thermodynamic rule, to measure a high-entropic system, we must use hyper-dimensional informational units.

The Democratic Primary candidate Beto O’Rourke is precisely such a hidden 2nd-place candidate thus far, who is indeed was polling close to 0% (now he is at 4%) in the primary although the votes he received in his Texas Senate run alone would place him near 3.5% of total votes across both parties, assuming no one in any other state voted for him and Trump was substituted for Sen. Ted Cruz. Due to risk-aversion, there is a tendency to vote for candidates who may win and avoid those who may lose. This causes initial polling measurements of elections to be skewed towards the more well-known candidates, since deciding upon the newer candidates early-on appears as a losing-strategy until they have gained traction. Yet, this presents a problem of risk-taking ‘first-movers’ in the transition of a new candidate to the front-line. Such explains only part of the low-polling for Beto, since Pete Buttigieg is also effected by the same time-lag for newcomers. When a candidate introduces a change to the status quo, we would expect a similar behavioral risk-aversion and resultant time-lag while the social norm is in the process of changing. While Pete’s gay-rights policy is already the norm for the Democratic Party, Beto’s Immigration-Asylum policy is not, given Obama’s record of a high-number of deportations, and thus we would expect Beto’s polling numbers to grow more slowly at first than Pete’s. Complex information to support this hypothesis is available by comparing the differential polling between the General Election and the Primary Election – Beto was found to be the Democratic Candidate most likely to win against President Trump, yet out of the top 7 primary candidates, he is the least likely to be picked for the primary, even though most Democrats rank ‘winning against Donald Trump’ as their top priority. This inconsistency is explained through the irrationality of vote preferences as only partially order-able (i.e. not-strict) thus far. Within the Primary race, people who may support Beto’s policies will not yet choose him as their candidate because of the newcomer and status-quo time-lag biases, although they believe he may be most likely to win over the long-run of the general election. In the General Election, Beto is the 2nd-place candidate across both parties under a rule of