Weekend Puzzle: Electoral Math

(Shamelessly ripped off Fivethirtyeight.com’s Riddler this week)

The State of Beaner is having its quadrennial gubernatorial election. Each of the State’s 10 counties is allotted a certain number of electoral votes: two, plus one additional vote for every 10 citizens (rounded to the nearest 10).

The names and populations of the 10 Counties are summarized in the table below.

Sleeper County113
Loki County214
Mark County315
Navy County416
Kimarie County517
Teeniner County618
Andrew County719
Shannon County8110
Kelly County9111
Aloha County10112

As you may know, under this sort of electoral system, it is quite possible for a presidential candidate to lose the popular vote and still win the election.

If there are two candidates running for Governor of the State of Beaner, and every single citizen votes for one or the other, then what is the lowest percentage of the popular vote that a candidate can get while still winning the election?

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