Here’s my latest Muse for Nature News. But while I’m in that neck of the woods, I very much enjoyed the piece on Dickens in the latest issue. Yes, even Nature is in on that act.
“The people who cast the votes decide nothing”, Josef Stalin is reputed to have said. “The people who count them decide everything.” Little has changed in Russia, if the findings of a new preprint are to be believed. Peter Klimek of the Medical University of Vienna in Austria and his colleagues say that the 2011 election for the Duma (the lower Federal Assembly) in Russia, won by Vladimir Putin’s United Russia party with 49 percent of the votes, shows a clear statistical signature of ballot-rigging .
This is not a new accusation. Some have claimed that the Russian statistics show suspicious peaks at multiples of 5 or 10 percent, as though ballot officials simply assigned rounded proportions of votes to meet pre-determined figures. And in December the Wall Street Journal conducted its own analysis of the statistics which led political scientists at the Universities of Michigan and Chicago to concur that there were signs of fraud.
Naturally, Putin denies this. But if you suspect that neither he nor the Wall Street Journal are exactly the most neutral of sources on Russian politics, Klimek and colleagues offer a welcome alternative. They say that the statistical distribution of votes in the Duma election shows over a hundred times more skew than a normal (bell-curve or gaussian) distribution, the expected outcome of a set of independent choices.
The same is true for the contested Ugandan election of February 2011. Both of these statistical distributions are, even at a glance, profoundly different from those of recent elections in, say, Austria, Switzerland and Spain.
Breaking down the numbers into scatter plots of regional votes lays the problems bare. For both Russia and Uganda these distributions are bimodal. Distortion in the main peak suggests ballot rigging which, for Russia, afflicts about 64 percent of districts.
But the second, smaller peaks reveal much cruder fraud. These correspond to districts showing both 100 percent turnout and 100 percent votes for the winning party. As if.
It’s good to see science expose these corruptions of democracy. Yet science also hints that democracy isn’t quite what it’s popularly sold as anyway. Take the choice of voting system. One of the most celebrated results of the branch of economics known as choice theory is that there can be no perfectly fair means of deciding the outcome of a democratic vote. Possible voting schemes are manifold, and their relative merits hotly debated: first-past-the-post (the UK), proportional representation (Scandinavia), schemes for ranking candidates rather than simply selecting one, and so on.
But as economics Nobel laureate Kenneth Arrow showed in the 1950s, none of these systems, nor any other, can satisfy all the criteria of fairness and logic one might demand . For example, a system under which candidate A would be elected from A, B and C should ideally also select A if B is the only alternative. What Arrow’s ‘impossibility theorem’ implies is that either we need to accept that democratic majority rule has some undesirable consequences or we need to find alternatives – which no one has.
Other considerations can undermine the democratic principle too, such as when a bipartisan vote falls within the margin of statistical error. As the Bush vs Gore US election of 2000 showed, the result is then not democratic but legalistic.
And analysis of voting statistics suggests that, regardless of the voting system, our political choices are not free and independent (as most definitions of democracy pretend) but partly the collective result of peer influence. That is one – although not the only – explanation of why some voting statistics don’t follow a gaussian distribution but instead a relationship called a power law [3,4]. Klimek and colleagues find less extreme but significant deviations from gaussian statistics in their analysis of ‘unrigged’ elections , which they assume to result from similar collectivization, or as they put it, voter mobilization.
A key premise of current models of voting and opinion formation [5,6] is that most social consensus arises from mutual influence and the spreading of opinion, not from isolated decisions. On the one hand you could say this is just how democratic societies work. On the other, it makes voting a nonlinear process in which small effects (media bias or party budgets, say) can have disproportionately big consequences. At the very least, it makes voting a more complex and less transparent process than is normally assumed.
This isn’t to invalidate Churchill’s famous dictum that democracy is the least bad political system. But let’s not fool ourselves about what it entails.
1. Klimek, P., Yegorov, Y., Hanel, R. & Thurner, S. preprint http://www.arxiv.org/abs/1201.3087 (2012).
2. Arrow, K. Social Choice and Individual Values (Yale University Press, New Haven, 1951).
3. Costa Filho, R. N., Almeida, M. P., Andrade, J. S. Jr & Moreira, J. E. Phys. Rev. E 60, 1067-1068 (1999).
4. Costa Filho, R. N., Almeida, M. P., Moreira, J. E. & Andrade, J. S. Jr, Physica A 322, 698-700 (2003).
5. Fortunato S. & Castellano, C. Phys. Rev. Lett. 99, 138701 (2007).
6. D. Stauffer, ‘Opinion dynamics and sociophysics’, in Encyclopedia of Complexity & System Science, ed. R. A. Meyers, 6380-6388. Springer, Heidelberg, 2009.