Asterix for President!

Discrete Mathematics Level 3

At the end of a presidential election, there is a 4 way tie. It's between the four candidates Asterix, Bernie, Clinton, and Donald. (Any resemblance to actual candidates is purely coincidental! :) )

It is to be decided by a final vote between three randomly selected citizens of the country.

The process proceeds as follows:

The voters are first all asked to decide between Asterix and Clinton. Clinton wins!

Then they are asked to decide between Bernie and Clinton. Bernie wins!

Finally, they are asked to decide between Bernie and Donald. Donald wins!

So, Donald is declared president.

However, if one final poll was taken, Asterix vs. Donald, what is the greatest number of people (out of the three) that could prefer Asterix over Donald?

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