Saturday, May 13, 2017

Politics and Soccer: When the Rules of the Game Really Matter

By William Hausdorff

It is now well known from one of the most painful of all US Presidential elections that getting the most votes is not enough to determine the outcome—it depends on the local rules (i.e., the electoral college) as to how those votes are counted.  As this was also readily apparent in the equally painful 2000 election, when Bush Jr stumbled into office against Gore, it’s easy to assume the local rules thing is yet another US idiosyncrasy. 

It may therefore come as a surprise to realize that the local rules for interpreting vote counts made (almost) all the difference in several recent, also momentous, European elections.  In other words, each could easily have gone the other way but for the specific, seemingly mundane rules in place in each country.  It turns out that there are many ways, from an electoral point of view, to crack an egg.

Perhaps you think you know what happened:  on the basis of a single vote, the Brits are abandoning the EU, the Turks are creating an executive presidential system that will dangerously concentrate power in the hands of their current leader, and most recently, the French chose a centrist, outsider President instead of a right-wing demagogue.  Perhaps you even recall the failure of a Hungarian referendum last October to keep refugees out of the country, despite EU requirements.  

Before getting into the details, let’s briefly consider the ideal ways to interpret vote counts from elections and referenda.

A simple majority seems most transparent.  I naively cling to the idea that my vote may be the one to put someone over the threshold.  I’m also aware that the need for supermajorities on every single issue can paralyze government, especially if it can easily be abused for purely partisan purposes.  Hence my longstanding distaste for a prominent role for the filibuster in the US Senate, as it requires a supermajority to break.

On the other hand, I like the idea that major changes to a system of governance or fundamental structural changes in policy require more than simple majorities (or pluralities). Amendment of the US constitution has only been accomplished 17 times in the 225 years since the Bill of Rights was enacted immediately after the Constitution itself, as it requires 2/3 majorities in both the House and Senate and ratification by ¾ of the US statehouses. 

This is a high bar, and generally seems appropriate.  On the other hand, the proposed Equal Rights of Amendment that simply stated

 Equality of rights under the law shall not be denied or abridged by the United States or by any State on account of sex

never became part of the Constitution, even though both houses of Congress passed it in the mid-1970s, as it was ratified by only 35 of the required 38 US States—and the narrow time window allotted ran out.

So while the bar should be higher for decisions of major consequences, one has to be careful not to place it too high.

An additional argument for raising the bar beyond a simple majority is that while no voting system is 100% accurate, a simple majority (or plurality) system is more easily prone to manipulation.  Beyond flagrant attempts to nullify ballots as seen in the 2000 Presidential election in Florida, in several US states there is the unceasing wave of voting rights restrictions, as well as campaigns where one side has much more money than the other.  It thus doesn’t seem difficult for such efforts to swing a few percentage points of the vote here or there. 

As a consequence, very close elections or referenda where a simple majority or plurality of votes wins are bound to be viewed with suspicion.  In contrast, when the hurdle is higher (such as a supermajority) for a significant reform to be made, and it seems difficult to chip away at a sizeable portion of votes, results in favor of a change may be more likely to be accepted.

What were the electoral rules in each of those elections? 

In the UK, then-Prime Minster Cameron was widely criticized for bringing Brexit to the voters, as it was seen as a politically cynical way to ward off UKIP efforts to siphon off Tory votes.  It obviously disastrously backfired (for him personally).  While there have been endless post mortems about the quality of the campaign arguments used, Labour party ambivalence, even voter understanding of the question, perhaps the real issue is the minimal threshold required. Of the 72% of the voters who turned out, only 51.9% voted for Brexit.  This equates to slightly more than a third (37%) of all eligible voters who made this monumental decision. 

One could argue that for a change of that magnitude—pulling Britain out of the EU, with huge economic and political consequences—the rules of the referendum could have been set in advance, either formally or informally by Cameron, so that some kind of supermajority of all eligible voters would be needed for the vote to be “valid”—e.g., 2/3 of eligible voters?

In the recent Turkish referendum, the vote was reportedly even closer:  of the 85% of the voters who turned out, 51.4% were for and 48.6% were against fundamentally changing the structure of government to a model with a strong executive presidency.  This translates into 44% of all eligible voters whose views “decided” the outcome. The narrowness of the margin, which could lead to President Erdogan (in power since 2002) only leaving office in 2029, is remarkable in the face of the tremendous obstacles put in place by the present government to the “No” campaign.  In addition, allegations of voting fraud filed by opposition parties were peremptorily dismissed by election officials.  

If the rules in Turkey, up front, had required a simple majority--but of ALL eligible voters--the referendum would have lost badly.

That is what happened in Hungary.  Last October, Hungarian Prime Minister Orban held a referendum that asked

Do you want the European Union to be able to mandate the obligatory resettlement of non-Hungarian citizens into Hungary even without the approval of the National Assembly?

Widely viewed as a referendum on closing the door to the 1,294 refugees that the EU had agreed would be Hungary’s share, the larger implications were about challenging the role of the nation-state within the European Union.  While 98% of those who voted were in favor, the result was considered invalid, as only 43.5% of the eligible voters actually turned out, well below the 50% threshold mandated by the “Fundamental Law of Hungary” (i.e., Hungarian constitution).  This result avoided a huge schism in the heart of the EU.

Another example where the structure of the electoral system provides some protection against spurious results is France, with its provision for a second run-off election between the two top candidates if no one gets >50% in the first round.  In the first round, the four top candidates each garnered between 19% and 24% of the votes.  Emmanuel Macron barely emerged with a plurality of votes: his 24% of the votes was marginally greater than the 21.3% of the votes obtained by Marine Le Pen of the xenophobic National Front. 

It is not difficult to imagine any number of events (another terrorist act; a Russian/Wikileaks release that was better timed; intimations of personal scandal; bad weather on voting day) that could have reversed those percentages.  In that case, and if the system had been designed as a single round, Le Pen would be President. 

Instead, in the second round Macron’s 66% to Le Pen’s 34% showed that Le Pen was actually widely unpopular among the majority of French voters, easily withstanding the Wikileaks election eve surprise—which in any case were not widely disseminated.  

How do these results compare to the US election?  Just to remind us, in none of the following four swing states did Trump even get a majority of the popular vote from the 55% of the eligible voters who turned out, yet of course he collected ALL the electoral votes from each state.   The popular margins were razor thin:


A tremendous amount of weight is vested in these relatively trivial margins representing the wishes of barely one quarter of eligible voters. 

Some attempt to take into account the margin of the popular vote within each state, or the absence of a majority of voters—for example, assignment of electoral votes within a state in a matter proportionate to the popular vote—could minimize relatively small perturbations due to chance, fraud, voter suppression efforts, even Russian interference.  Such reforms would thus help mitigate the divisiveness and rancor that accompanies every close Presidential vote.

Why do the Americans, British, and Turks put up with this?  I wonder if there are clues from how certain decisions are made/or not--in professional soccer.  (Please bear with me.)

In that sport, most games are extremely low scoring
--> (averaging <3 goals per game by both teams together), and thus a single goal can easily be decisive.  The rules say that a physical foul committed by a defensive player in the rectangular penalty area surrounding the goal necessitates a penalty kick.  These kicks are successful >75% of the time. 
Yet a single referee, continuously running up and down the entire length of the field, is tasked with awarding or not a penalty kick based on his/her evaluation of the behavior of what could be as many as 11 defensive players jostling with their offensive counterparts in the penalty box at a given time.  The referee is not aided by any other official nor by video replay.  

To an outside observer not steeped in soccer’s traditions as a youth but who has enjoyed watching many games, it seems obvious to me that the rules vest too much power in a single individual.  His/her decision, after all, can be literally game-changing.  Yet I’m unaware of any serious effort to examine this issue.

It’s not just a matter of becoming aware of the rules.  Soccer fans I’ve spoken with greet the suggestion of ANY kind of reform with disdain—it’s “tradition,” they say, for the referee to have free rein.  Similarly, it could be just “tradition” that keeps election rules favoring simple pluralities for momentous decisions the way they are.

But with a little creativity, perhaps we can identify some sort of vested interests in the current situation.  At first glance, it seems difficult in soccer as the same fans who scorn reform seem likely to be on the losing end of maddening miscalls or non-calls as often as they are on the winning end.  But I wonder if the richest, most influential soccer teams leave huge decision-making power in the hands of referees as a “bet” that referees will generally not make those admittedly subjective, unreviewable calls against the most popular teams when it really matters. 

Conversely, it may be those who are most efficient at manipulating elections through funding last minute fake news blitzes, or finding ways to suppress minority voter turnout, who would benefit from rules placing disproportionate weight on small voting margins leading to major decisions.  President Erdogan, after all, set the rules in Turkey.  I’m just wondering.


David Ricardo said...

Interesting post.

Here is the way a statistician would look at voting. Voting is a sample of the population. In the U. S. it is a sample twice removed from the population. The actual vote is a sample of the registered voters and the registered voters are a sample of the population. But the critical question is not participation, it is whether or not the actual vote reflects the population position. If it does then how many voted is not relevant. If 50% plus 1 is required then if only one person voted but that person voted the same way that the 50% plus 1 would have voted if everyone voted, then the result is valid.

The reason we want a large voter turnout is because statistically speaking, the larger the sample the greater the probability that the sample mean will reflect the population mean. Alternatively, the smaller the turnout the easier it is to ‘rig’ an election in which the actual vote or sample is not the same as the population result and is sufficiently different that the outcome is changed.

Republicans understand this far better than Democrats and have used their positions of power in state government to effectively ‘fix’ the vote by distorting the sample. This is done by a variety of means such as fewer polling places in Democratic precincts, ID requirements that are biased against Democratic voters, etc. In North Carolina where I reside the campaign to distort the sample was strong, open and blatant.

Finally, in the surprise results of the 2016 election most people concluded that somehow the polls had been wrong. It is entirely possible that no, the polls were not wrong, the samples of the population mean (actual votes) in states like Michigan, Pennsylvania and Wisconsin were statistically biased and different from the population mean. Trump may be President solely as the result of a statistical anomaly or the fact that voter suppression in key states produced a result different from what the population wanted

William Hausdorff said...

Thanks for your reflections. As you note, from a purely statistical perspective the size of the population sampled doesn't really matter, it's the representativeness of that sample in reflecting the larger will of the population. And that is an important consideration in judging the fairness of the results.

And I think your comments on Republican attempts to distort the sample are to the mark. The smaller the sample, the easier to distort.

At the same time, there is another consideration I think, which tempers the relevance of the statistical argument. Those who choose to vote are almost by definition not a random sample of the larger electorate. Choosing not to vote (or not even to register) is often a deliberate act, as exemplified by the concerted (and successful) popular effort in Hungary to discourage people from voting and therefore nullify the validity of the referendum.

For this and other reasons I think it is easier to argue that a vote in favor of a major change reflects "the popular will" if at least half of the electoral age population actually affirmatively chose it.