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Seeing Elections Through a New Lens

by Ricardo Pachon
5 minutes read

The image at the top of this post: Can you guess what it is? When I see it, its texture and volume make me think it could be some kind of stone, not exactly spherical but rather like the shape we recite in school to describe the Earth: flattened at the poles and bulging at the ends. Or maybe it’s a fruit, like a pumpkin…

Here’s a hint: the photo shows the side view of an object carved in wood. The next two images will show the front and top views of the same object.


Can you form a better idea of what the object is? If you connect the three images, you’ll realize it’s actually a bowl.

Now, which of the three photos is the correct one? The question doesn’t make much sense since all three capture a real side of the object we want to understand. The front view might have the most information, but we need the other two to reconstruct the three dimensions in our minds. The first image I showed in this entry—the side view—has the least information, exaggerating the height but confusing us about the length. And in any case, from these photos alone, it’s difficult to know how deep the bowl is inside.

A few days ago, I wrote a post summarizing the results of a preference survey for this year’s elections in Colombia. I received responses from 252 people who ranked five candidates plus a blank vote in order of preference. Each preference chain assigned a certain number of votes to each candidate based on their position. To obtain a collective view, all the votes given to the different candidates by the 252 respondents were added up.

Depending on how many votes are assigned to each position, you get different electoral systems, and the uncomfortable observation is that their results can be completely different from each other. For example, from the survey I obtained the following orders of preference using five different systems (using the nomenclature “Tom > Mary” to say Tom is preferred over Mary):

Duque > Petro > Fajardo > De La Calle > Vargas Lleras > Blank

Duque > Fajardo > Petro > De La Calle > Vargas Lleras > Blank

Fajardo > Duque > Petro > De La Calle > Vargas Lleras > Blank

Fajardo > De La Calle > Vargas Lleras > Duque > Blank > Petro

Vargas Lleras > Blank > De La Calle > Fajardo > Petro > Duque

It would seem that the five results contradict each other. The first chain, in particular, is obtained using the plurality system, which is what we use in our elections, and in which we only consider the candidate we prefer most and discard the rest.

Which of all these results is correct? Each result corresponds to a snapshot of what the group of respondents thought. They are all correct, as each one shows a different angle of the object we want to understand. But as with the photos of the bowl, one photo does not necessarily provide enough information to correctly reconstruct the object. The imposition of using a plurality system to choose our governors is no more arbitrary than deciding to only take side view photos.

The question remains: Is there an electoral method that is better than the rest? The analogy with the wooden bowl photo still applies. Take a look at the next picture:

Taking the photo diagonally and at a certain angle helps solve many problems. Likewise, the Borda Count or the Condorcet method are electoral systems that tend to introduce fewer distortions.

However, we can forget about having a perfect electoral system one day, one that we can always use with the peace of mind that we are not recording a misleading image. And this we know with mathematical rigor: Kenneth Arrow, whom I had already mentioned in a previous post, managed the feat of proving that any electoral system one can invent will always have a blind spot that manifests as electoral paradoxes. Translated to the world of photography, Arrow’s impossibility theorem tells us that if we always aim our camera from the same angle—and no matter which angle it is—there will always be objects that we will not be able to represent correctly.

We, the voters, may have free will and choose the candidate we want. What is striking is to discover that fate is encoded in the particular electoral system that has been imposed on us.

Can we design a democratic system to choose rulers in which we incorporate something more than just a single rigid and incomplete photo of what the people manifest?

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