How to improve the voting system? | Mathematics and democracy

Elections in Argentina, as happens in most countries of the world, have a peculiarity: many times a candidate who does not obtain the majority of votes wins. Said in these terms, it is obvious that something is wrong. If the goal is to check the population to find out what preferences they have, the method we use today does not solve the problem. Even more: behind an alleged legality there is an argument that takes away its legitimacy. I explain.

To avoid naming names and thinking about the problem from a theoretical point of view, I will use letters to name candidates. Suppose there are five candidates for the presidency of the nation. In our country, voting works like this: whoever gets the most votes is elected to office. Of course, if any of the candidates get half plus one of the votes, they must undoubtedly be the one in the position.

But what if that doesn’t happen? It could be that the elections had these results (as a percentage):

A 38%

B 26%

C 14%

D 12%

AND 10%

In this case A would also win and without having to participate in a second round (or ballot). It is that between the first and the second there is more than 10% of distance *. Case closed: A won! If the difference between the first and second is less than that 10 percent, then there is a second round or ballot between the first two. However, the problem with this method is that if you add up the percentages of everyone who did NOT want A to be the winner, you get 62%. Is it right that whoever has more than 60 percent against wins? The answer seems obvious: no, that’s not fair. And how do you go about solving this problem? I’m sure there must be several ways, but I want to propose some (which is practiced in places like Australia, also in England and has been used in some states of the United States) What is it?

What is done is the following. Instead of putting a ballot paper in the envelope with the candidate you prefer to win, all voters will have the same ballot paper but with a box next to each name. The voter chooses a number from one to five and places it in those boxes. These numbers represent your order of preference. It goes without saying that he puts the number one in the box next to the name of whoever prefers to be the winner. But having chosen an order for the remaining four, he is doing more than meets the eye. It is as if he said (for example): “I prefer C to win, but if C doesn’t win I prefer him to rule E. But if we eliminate C and E I prefer A. And if we eliminate these three, I prefer B to be the winner”. Your ticket would look like this

C 1 B 4

E 2 D 5

A 3

Now join me here and let’s find out together how this method solves the problem I raised at the beginning.

At the end of the voting, the first choice votes for each candidate are counted. Of course, if one of them has more votes than all the others combined, he wins the election and the problem is solved. It would be like having more than 50 percent of the vote. But now the difference appears. If after this first tally there is no winner, the last person who finished last is eliminated. However, the will of its constituents continues to affect, how? The one they have put as second option is added to each of the four candidates as if they had chosen it first and the rest is distributed among the four candidates respecting the order in which they were chosen.

When you get here, the count is repeated and if there is any one (of the four remaining) who has the majority of the votes, they win. If not, the fourth one is eliminated, but the order chosen in their votes passes to the three candidates who remain in dispute. A new count occurs and if there is no winner among the three, the process is repeated. It is clear that at some point one of the candidates will end up with the majority of votes and be declared the winner, but now it can be said that whoever is elected to govern will be the one with not only the highest approval rate but also the highest rejection rate. low.

Returning to the initial example, candidate E has been eliminated, but 10 percent of his voters are taken into account, so that they are distributed among the remaining four. Let’s assume the list now looks like this:

A 42%

B 27%

C 18%

D 13%

Note that since 10 percent of the electorate had voted for E, that ten percent was distributed between A, B, C and D in this way: four percent for A, one percent for B, four percent for C and one percent for D. Even so, neither of them reaches an absolute majority and therefore the procedure is repeated and in particular without requiring a new vote. The data of the only one that was created is used. Now the one eliminated turns out to be D, but the 13% who had chosen it continues to have an impact on the following three: they are distributed in such a way that the list now looks like this:

43%

B 37%

C 20%

Since there is still no candidate that collects more than 50 percent of the vote, we continue with the same idea. Now C is eliminated but the 20% who chose him continues to have an impact. Suppose they prefer 15 percent to B and 5 percent to A. With these figures we reach the end of the election:

B 52%

A 48%

As we can see, the winner is B, who is the one who best expresses the preferences of the company. In this way, each voter not only has the possibility to choose who would like to win, but also has their vote intervene in punishing – in the end – some candidates over others.

As I wrote above, this system has been used in Australia since 1918 and in the House of Lords in Great Britain. In 2006, in the state of Minneapolis (where George Floyd was recently assassinated), the provincial legislature decided to adopt this method from that year and today it is used in some cities of California, North Carolina, Colorado, Maine and Maryland in the States. United. The curious thing is that every time the method was used, it was done for provincial elections and never for senior positions in the federal government.

Isn’t it time to rethink our voting systems and put them to a vote anyway? In this case it would be a sort of binary choice: “Would you be in favor of this reform or not?”

Yes, I ask you …

*Important clarification for Argentina. This note was written for any country in the world without taking into account the details of the electoral legislation of each. Therefore, the numbers were chosen at random for mere explanatory purposes. In our case it is obvious that to win in the first round, in addition to the 10 points difference, the first must exceed 40 percent.

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