34-state recount? Still improbable.

For Hillary Clinton’s campaign to optimize her concluding chance at a successful recount of the presidential election, it would be unwise to merely pursue the slipshod lane of fighting a judicial contest in select counties of 3 or 4 states.  Instead it would be better to annihilate any residual reputation from the two futile and tattering campaign bids and just endeavor a full recount in every state the Democrats lost (all 34 of them).  From a probability perspective, this makes things interesting because we can have many more permutations of states that would need to successfully be overturn in Hillary’s favor, in order to convert at least 37 electoral votes.  Unfortunately though, even if we assume that there is a high 10% chance for succeeding in each of these 34 states, there would still be only a less than 1 in 3 chance of successfully flipping the >37 electoral votes needed.  And it is all downhill from there, since the 10% chance in each state is nearly an upper-bound, charitable supposition for a blended probability.  Given that this would imply something on the order of 1 in 7 voters would simply have their vote 2^nd guessed by the Electoral College, and replaced with a 50/50 coin flip towards Hillary!  Also the empirical recount odds when looking at this throughout U.S. history reflects a far lower overall chance for Ms. Clinton (<15% in actuality of her breaking the electoral process in federal court, let alone <5% chance of an eventual victory).

 
Of course many things could alter the arc of things, and they all of course lead to less optimized odds.  For example we can assume that not all 34 states make sense for a recount, due to their voting mechanism and large (and historically consistent) Republican lead given to Donald Trump.  So let’s say in this case we simply exclude Texas and Florida form consideration.  And only recount the 32 (less populated) residual states.  Suddenly then the odds of a victorious outcome are now halved (from <1:3 we stated above, to ~1:6).  Of course we can jointly simply beef up the chance in each state by 50% (to 15%, from 10%).  And even so, the overall chance for a successful recount outcome is less than ½.  That must be gloomy! 

See a small and bighearted variety of overall outcome distributions are for recontesting 34 states (at 5% odds in each state, and at 15% odds in each state).  Note that the latter would give Hillary a 55% probability of winning (i.e., >37 votes in the charts below), though even the former 5% odds per state is apt a magnitude larger than reality (and the former has only a 10% overall chance of winning).

 

It’s simply tricky with a country where more than 100 million people vote, and where even the smallest electoral states possible for recontest have had a turnout this year of over a ¼ million voters.  Therefore closing even a 10 basis point margin is probabilistically low, let alone overcoming a multi-percent margin we have in many of the states above.  Even if there were a con in the voting mechanism (as opposed to the official justification for the recounts), one would have to assume it was fully rampant that it would cover multiples of the number of counties that were estimated by the disgracefully-botched Hillary Clinton statisticians (Nate Silver) and lawyers when explaining why their side is recounting.  While these legal strategists and data scientists further ruin their standing, so far the odds diminish with each day the recount data comes in worse than expected for Hillary.