This is how I derived the given formula.
If we want to elect one candidate, S shares must go to him, where S is greater than all other shares divided by 11 (which is the least number of candidates vying for a position). That is,
S > (5M - S)/11
From this, we get S > 5M / (11+1). Thus S must be at least [5M / (11+1) ] + 1 = 416,667.667 . Rounding off we get the 416,668.
Same reasoning if we want to elect 2 members of the board. We should have T shares, so that for each of our 2 bets:
T/2 > [5M - (T/2)]/11
=> T > 2*(5M) / (11+1)
Therefore we need T to be at least [2*(5M) / (11+1)] +1 = 833,334 shares.