British Columbia: Voting on the Voting System

The Proposed Single Transferable Vote (STV) System
One of the big headlines in Canada during late spring of this year was the referendum being held in B.C. to switch to a STV system.  Currently, the province utilizes a "first-past-the-post" plurality system.  As we learned during our class on Strategic Voting, the STV system allows each voter to rank their preference of candidates.  This proposal further changes the mechanics of the system by grouping ridings into districts.  As such, a vote can determine who is elected to a block of 2 to 7 seats (dependent on your district's population.  The process is depicted in the chart below. 

The strength of this system over the existing plurality system is that it avoids the need for strategic voting since the system in itself is self-optimizing.  Stategic voting under the existing system may suggest that even if you support the NDP party in this riding, you should vote for the Liberal Party because they have the best chance of toppling the Conservative candidate.  With STV this process is applied automatically. 

Organized Strategic Voting
This referendum was held in conjunction with the B.C. provincial election, which gives is direct insight into the types of strategic voting that occur in a plurality system.  Our text mentions that in a plurality system strategic manipulation of votes can result from the introduction of a spoiler--a late entrant in the game who can shift the votes away from the leading candidate.  For this election in B.C., we see another strategic manipulation called vote swapping. 

One popular website that employed vote swapping was http://www.votepair.ca/.  VotePair is a proponent of the STV system which it advertises as the solution for "eliminating the need for vote swapping".  The system works as follows:

Let's say that your preferred candidate has no chance of winning in your riding. You can swap that vote out with someone else in the group who will vote for your party in a riding where it has a chance to win, while you will vote for the party that has the best chance to stop your least favorite party in your riding. 

Dominant Strategies
Although vote swapping is gaining wide spread popularity, it is built on trusting that the person your are paired with will execute on their promise to vote for your candidate  The dominant strategy for each individual is to lead the other to believe they will vote according to what they promised on VotePair, and then vote for their own personal preference.  However, if both players follow their dominant strategy then they will lose the benefit that vote swapping provides.

Looking at it from another perspective though, if you intend to cheat/lie (and not carry out the promised vote), then you really have nothing to lose by participating in vote swapping.  In the best case you will get 2 votes for your party (yours and your vote swap partner) and in the worst case you will still have your 1 vote for your party!


For more information on the STV system that was proposed in B.C. go to:
http://en.wikipedia.org/wiki/BC-STV

Prisoner's Dilemma: A Hockey Player's Perspective on Visors

As a Canadian, no blog would be complete without a mention of our favorite national pass-time--the great sport of hockey!  I was watching a game recently where a player sustained a bad injury close to his eye as he was hit with top end of a hockey stick.  Luckily, the stick was an inch away from creating a debilitating eye injury.  This did bring a question to my mind though on why all hockey players don't have visors on their helmet?  According to Wikipedia, only 60% of NHL players have visors.  I did a little bit of digging and found that there are a number of reasons why a player would not want to wear a visor, among them the issue of visibility stood out.  Hockey players not only complain that visors reduce their peripheral vision, but that the visors also attact ice debris and water specs (during hard stops) that create distractions. 

This issue can be structured as a Prisoner's Dilemma.  Let's say we have 2 hockey players: Brule and Fisher.  These individuals play center for the Oiler's and Senator's respectively.  Both players value scoring goals over safety and believe that they perform better without a visor on.  For each the payoffs are as follows:

• 4 - Opponent wears visor and I don't: In this case I have an advantage since I will have better visibility
• 3 - We both wear visors: In this case we both have an equal handicap and we gain the safety provided by a visor
• 2 - Neither of us wears a visor: In this case neither of us has a handicap, but we are more likely to get injured
• 1 - I wear a visor but my opponent does not: In this case I am at a disadvantage to my competitor

Laying this out in a game table we have:

The dominant strategy for both Brule is to select No Visor.  This is also the dominant strategy for Fisher.  As a result both players end up at "No Visor".  If the players can both agree to wear a visor, they can increase their payouts from 2,2 to 3,3.  Of course, this is a rather unlikely scenario.  A more realistic way for the players to get a higher payout is if the NHL placed a mandate requiring all hockey players to wear a visor (with the exception of goalies who wear cages!)

For more information on visors and associated statistics, please see:
http://en.wikipedia.org/Hockey_helmet

The Dead Hand – A Destructive Conditional Strategic Move?

Earlier in the semester I read an article called Inside the Apocalyptic Soviet Doomsday Machine in Wired Magazine (September 2009 Edition) that touches on some interesting aspects of game theory.  The article discusses Perimeter--A doomsday machine that guarantees "an automatic Soviet response to an American nuclear strike." In the event that a nuclear attack is detected on Soviet soil, the system unleashes an arsenal of nuclear missiles directed towards the US. 

This article ties well into the readings and the class we had on strategic moves. It touches on first move, credibility, deterrence, conditional strategic moves, and the response rule.

From the Soviet perspective, the US had made the first move in escalating the Cold War by announcing that they were going to pursue the SDI program.  SDI was a space-based missile defense program that could protect the US from a large scale nuclear attack.  Tying this back to the course, this step constitutes a first move because (1) it is observable, and (2) from the Soviet perspective it is irreversible.   The Soviet's knew that the US was building more arms, so from their perspective this was a credible move and an indication that the US would soon attack.  From Reagan's perspective, the purpose of SDI was to achieve deterrence; he believed it would "bring about lasting peace."  The disconnect between the implied intent and the understood intent was the basis for Soviet's reason to create the Dead Hand.

Essentially, the Dead Hand could be the Soviet's conditional strategic move.  The Soviet's move is conditional upon America's actions; if America does not attack then the Soviet's won't launch their nuclear warheads, but if they do attack then the Soviet's would retaliate.  The retailiation in this case is the response rule. This threat of mutual harm could serve as a deterrence.  Of course, I say could in these cases because based on published reports, it does not appear that the US ever knew about the Dead Hand.  As the article states "the whole point of the doomsday machine is lost if you keep it a secret!" 

Was this a self defeating strategic error?  Or did the Soviet's take game theory one step further and play this strategic move to deter their own military from conducting a premature nuclear launch?  By guaranteeing retaliation it would lessen the chance of any military officials making a preemptive strike.