NewScientist Magazine Article on Vote Theory Misleading and Damaging

The piece linked communicates numerous misunderstandings of both vote theory as well as political systems. I directly communicated with the author who explained to me that it is difficult to convey these principles to a readership with  an assumed limited math background. There is also limited space. He states his claims are upheld by journals, yet NewScientist chooses to save space by omitting references.

Following is a detailed criticism. References to article are in italics and bulleted. . . .

• “Making elections fair is more a matter for mathematicians. . . . What they have not done is come up with the answer. With good reason: it probably doesn't exist.”

Kenneth Arrow's Impossibility Theorem states: “. . . my theorem is not a completely destructive or negative feature any more than the second law of thermodynamics means that people don't work on improving the efficiency of engines. We're told you'll never get 100% efficient engines. That's a fact--and a law. It doesn't mean you wouldn't like to go from 40% to 50%."

According to Arrow, the fatalism described in the article violates his theorem. Further, his theorem is most relevantly applied to single office elections where inaccuracies in the winner selection can produce the greatest discrepancies from voter desire. Given the context of this article, plurality is the victim--PR is not. Even more, if one really wants to elect legislatures via single office positions, range voting sidesteps Arrow's theorem. The technical and minor exception can be found in Gaming the Vote, pg 254.

• “This system [plurality] scores well on stability and accountability, but in terms of mathematical fairness it is a dud.” . . . “What's more, proportional systems tend to produce coalitions of two or more parties, potentially leading to unstable and ineffectual government - although plurality systems are not immune to such problems, either”

So, plurality scores well on stability and accountability, yet it is not immune to unstable and ineffectual government? Even so, PR systems are worse? This is false according to the Political Instability Index. Eight of its top ten most stable countries use PR democracies. Further, in plurality small changes in voter opinion can drastically change representation. But in PR systems small voter changes lead to proportionately small representation changes. Unlike plurality, this characteristic of PR exemplifies stability by definition.

• “So we are left to make the best of a bad job. Some less fair systems produce governments with enough power to actually do things, though most voters may disapprove; some fairer systems spread power so thinly that any attempt at government descends into partisan infighting.”

Though not defined as such, dissenting groups within plurality parties may as well be another party. Does having two parties really expedite the legislative process? References other than lots of people repeat this? Do the passed policies actually represent the voters’ wishes?

This article also propagates a myth that PR systems will lead to small ineffective parties. This ignores the fact that many countries use thresholds to mandate a minimum level of support in order to gain any seats. This threshold for PR systems prevents especially small parties. Even more, some countries with many parties actually do excellently on the Political Instability Index.

• “But large constituencies weaken the link between voters and their representatives [in PR].”

It is unlikely in plurality that a particular constituent even voted for the representative. Most would not call this incongruence in ideology a “strong link.” But in a PR system almost all constituents have someone who represents them ideologically. Popular PR systems such as STV go even further by affording more geographic representation in addition to ideological representation. You don't even mention this.

• “Candidates [in PR] are often chosen from a centrally determined list, so voters have little or no control over who represents them.”

This is a falsehood. Open lists are used in many PR countries such as Brazil, Chile, Denmark, Finland, Norway, Sweden, Switzerland. All STV countries are also (obviously) "open list."

• “Proportional representation has its own mathematical wrinkles. There is no way, for example, to allocate a whole number of seats in exact proportion to a larger population.”

A reasonable observer will easily note that the small variance in proportionality under a PR system is a stark contrast versus the highly distorted outcome in a plurality system. Unlike PR, plurality systems further compromise fair representation by hindering voters from voting genuinely given an alternative exists. This fear of a throwaway-vote further disfigures the proportionality of plurality systems. Even without dishonest voting, plurality violates voting criteria to no end and to devastating degrees(Individual Visual; AND Bayesian Regret). Clearly, the inexactness of PR is nothing compared to plurality’s abysmal attempt at proportionality.

I recommend Gaming the Vote for a discussion on voting systems: