Instead of going to all the expense of flipping a coin, though, you could just take the person who seemed to get the most votes (after you've counted them all really hard to make sure you're within the margin of error). Just an arbitrary rule, no biggie.
Or have a runoff election, or have instant-runoff voting. Having elections determined by real or statistical coin-flips undermines the (important) story of self-rule.
The candidates agree, and the winner and loser both accept the outcome, works for me.
Your link to a place where they used a coin flip isn't disagreeing with him (nor really the grandparent, who wasn't claiming that you can't use a coinflip, but rather that you shouldn't use a coinflip).