Home Elections Decoding Preferences: A Simple Electoral Survey

Decoding Preferences: A Simple Electoral Survey

by Ricardo Pachon
7 minutes read

Last week, I conducted a poll on the candidate preferences for this year’s first round of presidential elections in Colombia. Survey participants could rank the five candidates, plus the option of a blank vote, according to their preferences—from their top choice (assigned the value 1) to their least preferred (assigned the value 6). The following image depicts two examples of how the responses could look.

In the left-hand example, the preference was for Petro, followed by Fajardo, a blank vote, Vargas Lleras, De La Calle, and lastly Duque. In the right-hand example, the preference was for Duque, followed by Vargas Lleras, a blank vote, De La Calle, Fajardo, and lastly Petro. To simplify reading in this post, I will use the notation “Person A > Person B” to indicate that Person A is preferred over Person B. Thus, the example from the left in the previous image can be rewritten as:

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

and the example on the right as:

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

The survey was completed by 252 individuals who saw it on my Facebook profile or that of some friends who kindly shared it (many thanks to them!). I knew the sample was going to be small and biased to make any forecasts about what would happen on May 27th, but that didn’t matter to me because my goal was something different. My intention with this survey was to conduct an initial experiment on the type of results we can obtain when we incorporate the spectrum of our political preferences into elections.

The simplicity of our choices masks the great complexity that arises in a society where individuals do not see politics in black and white but in a spectrum of colors. Beyond whether one supports Petro or Duque, the way someone perceives the rest of the candidates can provide very valuable clues about the type of society they wish to live in. For instance, compare the earlier right-hand example (Duque > Vargas Lleras > Blank > De La Calle > Fajardo > Petro) with another possible preference order:

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

Both individuals support Duque, but can you feel that there is something different between them? Can you identify the types of desires and fears each might have? Can you imagine what these two people are like? Perhaps you know them? Tell me what you think about these two individuals in the comments section.

A basic exercise in mathematics shows that there are hundreds of such chains when there are six candidates (extra points to those who say the exact number), but before conducting the survey, I thought that in real life people would only have a preference for a few of these. The surprise came when I counted that among 252 people, 86 different chains of preferences were formed, many marked by just one or two individuals.

Now comes the million-dollar question: How can we make sense of all this information? The key here is to find some way to group the different responses to get a picture of the electorate as a whole. Here are some options:

  • Start with the system we use in our elections, where each person only votes for one candidate. We can replicate this using the chains of preference, taking only the first one, giving this a vote, and discarding the rest of the candidates (what a waste of information!). We sum all the votes each candidate received and order them from highest to lowest. This method of election is known as the plurality system. When I do this, the candidates in my survey were ordered as follows:

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

  • What if we try to incorporate information about the second preferred candidate? We could reward them in some way, perhaps by giving two votes to the first candidate of our preference, and one to the second. To calculate the totals, we sum all the votes each candidate received and order them from highest to lowest (of course, now there will appear to be more votes than voters, but that doesn’t matter, what matters is how the candidates are ranked at the end). When I do this with the results of my survey, I now get the following order:

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

       Look! Petro and Fajardo have swapped positions!

  • What if we incorporate the third preferred candidate? We could give three votes to the first candidate of our preference, two to the second, and one to the third. The picture we get again is different:

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

  • Why not then give votes to the first five candidates of our preference, from highest to lowest, five, four, three, two, and one vote respectively, but none to the sixth? This method of voting is known as the Borda Count and what we obtain now is again a different order:

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

  • Finally: What if instead of rewarding the most preferred candidate, we penalize the most disliked? Thus we give one vote to the least preferred candidate, sum all the votes each one received, but order them from the fewest number of votes to the most. Although it might seem strange, this is a respectable electoral system known as the anti-plurality method, and by doing this I obtain the following order:

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

I hope that the reader who has reached this point feels a bit uncomfortable with all these results. We start with the illusion of being able to incorporate a broader spectrum of preferences than we currently have, but what we get is that the results fluctuate depending on the weight we give to each candidate. How can we interpret all these results? Who should go to the second round? Which of all these results is the correct one?

The answer is that all these results are correct. None can claim to be more natural than another. All are equally arbitrary, including our current plurality system. It’s disconcerting, and I will have to explain this in detail, but that will have to wait for the next post.

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