Marine Le Pen can breach her glass ceiling: The drastic effect of differentiated abstention

Ranges of differentiated abstention are shown to reverse an "exact" poll estimate on voting day allowing the minority candidate to win the election. In a two-candidate competition A and B with voting intentions at $I_a$, $I_b=1-I_a$ and respective turnout at $x$ and $y$, there exists a critical value $I_{ac}$ for which $I_{ac}<I_a<\frac{1}{2}$ yields an actual election outcome $v_a>\frac{1}{2}$. The reversal may occur without any change of individual choices. Accordingly, for a set of turnouts $x$ and $y$ the minimum voting intention $I_{ac}$ required for A to win the final vote can be calculated. The various ranges of $x$ and $y$ for which $I_{Ac}$ is smaller than the expected 50\% barrier are determined. The calculations are applied to the coming 2017 French presidential election for a second round scenario involving the National Front candidate Marine Le Pen against either the Right candidate Fran\c{c}ois Fillon or the Center candidate Emmanuel Macron. Several realistic conditions are found to make Marine Le Pen win the election despite voting intentions about only 40-45\%.