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January 25, 2011

Minority Can Elect BC Liberal Leader

An example is provided here which proves that the weighted voting system which the BC Liberals may adopt for their election of the next premier allows a minority of BC Liberal party members to win the vote. Right click here and choose save target as to get a spreadsheet with the numerical example which shows that a candidate with 47% of the popular vote can win the 4251 weighted votes necessary to become BC Liberal party leader and premier.

Some of the political spin around the voting system is around the issue of whether it gives more voice to rural ridings or whether it gives more voice to ridings that don't vote Liberal. Sorting out that spin requires a list of the 85 constituencies showing the number of members in each; those under the average would have more weight under the proposed system and those over the average would have less.

The numerical example provided here is a service to inform delegates to the Liberal's February 12th convention. It steps away from the political spin and deals with the simple mathematics of the proposed weighted voting system. Instead of referring to the constituencies by names like Prince George - Mackenzie or Vancouver - West End, the example numbers the constituencies 1 through 85. The Liberals expect to have about 60,000 members by the time sign-ups are cutoff on February 4th. That is an average of about 700 members per constituency; of course, some will have more and some less which is why an argument is made about a weighted voting system.

For the purpose of this example, assume that constituency number 43 has 700 members and that as constituency numbers increase from 44 to 85 ten members are gained for each step and that as constituency numbers decrease from 42 to 1 ten members are lost for each step. This produces an example for our purposes where constituency 1 has 1120 members and constituency 85 has 280 members.

For our argument assume that after several rounds of voting where second and third preferences are redistributed, on the final count we have a candidate we'll call George who receives 60% of the vote in constituencies 43 through 85 but only 40% of the vote in constituencies 1 through 42, the ones with the larger number of members. As shown in the accompanying spreadsheet, our example has 59,500 Liberal members. In the final count, George receives 28,014 votes overall, 47.1 per cent. Because of the weighted system, which gives each constituency 100 points and each candidate the percentage of those points that they receive in the vote in each constituency, George wins with 4260 points; 4251 are needed to win.

Other examples are possible and as you play with the spreadsheet you can see that a minority doesn't always win, but the weighted vote system makes it possible for a minority to win. Just like the 1996 provincial election!