Chapter 17.2, Problem 41PS

HISTORICAL QUEST Article $7$ of the French constitution states, "The President of the Republic is elected by an absolute majority of votes cast. If this is not obtained on the first ballot, a second round of voting must be held, to take place two Sundays later. Only two candidates may stand for election on the second ballot, these being the two that obtained the greatest number of votes in the first round.”

The $2002$ French presidential election incumbent president Jacques Chirac (center-right political party) and Prime Minister Lionel Jospin (Socialist party) were shoo-ins for the second round, but the strength of the extreme right candidate Jean-Marie Le Pen was unanticipated. Here are the results of the first-round voting (rounded to the nearest percent):

$\begin{array}{cc}\text{Jacques}\text{Chirac}& 20\%\\ \text{Jean-Marie}\text{Le}\text{Pen}& 17\%\\ \text{Lionel}\text{Jospin}& 16\%\\ \text{Others}& 47\%\end{array}$

These percent are of the votes cast. It was estimated that $28\%$ of the voters abstained.

a. Who are the two candidates in the runoff election?

b. Jean-Marie Le Pen is described as racist. Here is statement from A la francaise forum:

“Today, the strongest feeling I have is SHAME. For the first time in my life, I’m ashamed to be French. All of the values that I believe in (culture, tolerance, integration …) have been scorned and denounced by $17\%$ of my country’s voters.”

Comment on this quotation in light of the fairness criteria.

c. The vote in the second round of the election was:

$\begin{array}{ll}\text{Jacques}\text{Chirac}\hfill & 82\%\hfill \\ \text{Jean-Marie}\text{Le}\text{Pen}\hfill & 18\%\hfill \end{array}$

It was estimated that $19\%$ of the voters abstained for this ballot. Give at least one possible change in the voting preferences to account for the first and the second votes.