[tbontob]

The more I think about it, the more attractive it seems.

For example.

Candidate A has a platform which 60% of the voter approve.

Candidate B has a platform which 40% of the voters approve.

Normally Candidate A would win.

Then comes the spoiler. Candidate C has a platform which had the approval of 25% of voters who would normally approve of Candidate A's platform.

So, you have
Candidate B 40% of the votes
Candidate A 35% of the votes
Candidate C 25% of the votes.

So, candidate B would normally win.

But under the suggested voting method, Candidate C would be eliminated and his votes would be distributed in accordance with the voters second preference, which in this case would be A.

So, A wins with 60% of the votes.

Now, normally it would be more complicated than this with some of the votes going to B, but it does illustrate the point.