Blogs, Modeling

Election Day

Today the midterm elections are taking place.  As a country, we are going out and placing our vote for the next leader of our district or state in congress, senate or in any number of local government roles.  Well, historically,  around 40% of the nation is going out to vote today.  I hope that you’ve taken the time to go vote today, so that your voice will be heard.

While we are voting, we should think about how our votes are counted and tallied in determining who will win these important elections.  In order to do these, I wanted to look at different voting techniques and the goals of each of these.

Most votes

The first thought that comes to mind when speaking about a voting techniques is that the person that receives the most votes should win the election.  In and ideal democracy, this would look like everyone that wanted the position would put his/her name forth, the public would come together and everyone would supply a vote.  Then the person with the most votes wins.  If we just stop thinking about it, that seems fair.

However, we saw this play in out in the 2016 Republican Primary as we had a large list of people trying to get the nomination.  What we saw unfold was probably one of the most democratic election processes that you could have.  However, in this large field, many candidates weren’t differentiable from each other.  As such, these candidates tended to fight over shared votes, with people making choices based on small differences in candidates.  On the other hand, Donald Trump was so distinguishable between everyone else that the primary became a contest of Trump against the rest of the field.  Since the rest of the field was sharing votes, Trump could take in even a  small portion of the votes, but still get more than any other individual that was splitting votes across so many candidates.

We indeed have also seen this play out in presidential races, such as when Lincoln ran against two democrats Breckenridge and Douglas.  Here the votes were split and Lincoln won the presidency.  While we should now be thankful for this, and clearly it wasn’t the only reason, after the election the southern states seceded from the Union in anger at what occurred.  Now, in the election, suppose that Lincoln would have been running against only Douglas, would he still have won?  Or if he had been running against only Breckenridge, would he still have won?  While we could speculate, I just want to point out the possibility that this is why the political party nominate only 1 person for the presidential election.

Other voting techniques

Suppose that we have three candidates running for office, Hillary, Bernie and Donald.  With these, we then have 5 voters, and we will even have to voters rank the candidates in order to see how the election plays out in different circumstances.

Candidate / Voter 1 2 3 4 5
Hillary 1 1 3 2 3
Donald 3 3 2 1 1
Bernie 2 2 1 3 2

Note that here Hillary and Donald each get 2 votes to win.  If only looking at first place votes, we would then have a tie between these two that would likely be settled in a run off.  In this situation, Donald would win, because voter 3 would have picked Donald over Hillary.  However, if we had looked the rankings and assigned points, say 1 point for 3rd, 2 points for 2nd and 3 points for first.  Then all three actually end up tied for votes.  When comparing in a run off situation, we would have the case that Bernie would beat Donald, Donald would beat Hillary, and Hillary would beat Bernie.  While we don’t give rankings in an election, it is distinctly possible this is the situation we ran into in the last presidential election.

Therefore, what are the different ways we’ve already mentioned for ranking candidates?  Where are these used?

  •  We can have most popular out of all that run.
    • This is like a race where everyone enters the pack together and the first one across the line wins.
  • We can have a run off, where they face each other two at a time and loser goes home.
    • This is a playoff situation as we see in the NFL, NBA, MLB and March Madness!
  • We can all run against each other and tally wins at the end.
    • This would be like a round-robin tournament.  This is takes place in the initial round of the world cup, they then go to a playoff situation after that.
  • We can also have a hybrid thereof.

Note that in the above example, we do not have to have any agreement between these elections types.  While one person may win in a given situation, they may not win in another.  If we can find a voting method that will always give the same winner whether the entrants or ranked, or just the top vote counted, run all at once or each pair at a time, then this would be a fair voting technique.  That would be best wouldn’t it?

Well it turns out the only fair voting technique is to have a dictatorship where one person gets to decide the outcome of the race.  If such a person were perfect, that would be fine, however,

Absolute power corrupts absolutely.  -Lord Acton

Therefore, we would like to find a method that provides the best results possible.  Note that we have done such things in this country and our government is not a true democracy.  Instead, we incorporate voting techniques to arrive at a winner.

Our Government

State Elections

Instead of trying to understand the intricacies of the entire United States government I will instead focus on a few smaller examples in order to illustrate the process.  Therefore, suppose that we have only two candidates Rob and Deb running for dean of a school.  In this case, each person gets to vote, but the winner of each department gets all the votes for that department.  Therefore, we get something like

Math Physics Biology
Rob 2 2 0
Deb 1 1 3

In this situation, Rob will win because he won two departments.  However, Deb did indeed win the popular vote.  If we want a comparison to our government, this would be the situation with the House of representative.  Each state is broken up into district and each district picks a winner. While the winner of the district is by popular vote, each district gets to put a person in congress.  In this way, we can have a Republican controlled congress even if the Democratic party is more popular.  In general we would expect this to be the exception and not the rule.  However, if you can predict how everyone will vote, and you get to decide how the grouping are made, you can ensure that you will have more representatives despite having a lower popular vote.  Herein lies the truly disturbing problem in gerrymandering.  This is precisely what is going on, which is why there has been an uproar over the drawing of the districts.

Presidential Election

Image the above situation where each department votes.  However, instead of having equal people and equal votes, there are different numbers of people, and the number of votes the departments gets isn’t proportional to the number of people in the department.  For the last example, assume that there is only 1 person in the math department and 1 person in the physics department, and the biology department has 5 people.  As a weight, we divide the population by two, round up and add 2.  Then math and physics get 3 votes each and biology gets 5.  Now, suppose we have the following results

Math Physics Biology
Rob 1 1 0
Deb 0 0 5

Here, despite only getting 2 out of 7 votes, Rob would win because Math and Physics combined get 6 votes, while Biology only gets 5.  Therefore, if both people in Math and Physics agree on the winner the 5 votes from Biology won’t matter.

This is how the electoral college was designed.  The idea behind it was that each state was its own entity and therefore was entitled to power within the government.  In order to maintain some independent control, small states wanted to ensure they weren’t made to give in to the decision of larger states.

While this seemed like a huge issue at the time, there really haven’t been elections where large states tried to take on small states.  There have been plenty of states banding together for power, but generally this has been done regionally.  However, it does seem that this large verse small state has been working itself out recently.  In particular, the population of a city can be larger than an entire state. For example the current population of New York city is approximately 8.6 million (Wolfram Alpha).  This is larger than the population of all but 11 of the states (Wolfram Alpha).  Therefore, the large state-small state fight has become an urban verse rural population battle.  In this way, we have seen that in both the 2000 and 2016 elections that the candidate that won the popular vote did not win the election.


The issue of voting and determining a winner in an election isn’t actually as clear-cut as it may appear to be.  Under different criteria or voting circumstances, we can often end up with a different winner of an election.  Because of this, we should always continue to evaluate the countries voting practices to ensure that everyone has a proportional voice.  Even if the system we choose isn’t completely fair, we still need to participate.  Otherwise, we have no voice at all.

I hope you enjoyed the post.  If you did please be sure to like it below and share it on Social Media.   Have an opinion on the voting structure?  Please let me know in the comments below, I would love to talk more about it. 

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