In fact, I suspect there's a Superpac somewhere that would fund research showing the net effect it might have. Or some organization that would want to know what that does to algorithmic trading.
I'm guessing though, the likelihood of a bill like that making it all the way is pretty low.
The net result is that institutional investors (Goldman) won, retail investors (grandma) lost and spreads (the cost of trading) increased 9%.
I haven't been paying close attention, but I thought Bernie was contrasting himself against Hillary who is supposedly in the pockets of banks. That image doesn't really fit with such a policy.
"Has proposed a financial transaction tax which will reduce risky and unproductive high-speed trading and other forms of Wall Street speculation; proceeds would be used to provide debt-free public college education."
I'm trying to avoid getting into a debate about whether it's a good idea. If you think, though, it has some chance of happening...it does specifically become an "Open Problem in Quantitative Finance", which is what the OP is asking for.
The "open problem" I guess will be improving the existing tax avoidance software for traders?
 High speed trading is extremely non-risky. Look at graphs of the most extreme HFT incidents: https://www.chrisstucchio.com/blog/2012/flash_crash_flash_in...
don't big traders use HFT as a market advantage over retail?
One description of the HFT (from the always thought provoking Matt Levine): "It's an incremental efficiency improvement, with some opportunity for gamesmanship, that overall allocates some money out of the pockets of banks and hedge-fund managers and into the pockets of exchanges and HFT technologists."
That's basically correct. And as a bonus, the small retail investor buying twenty shares of Apple now gets his shares very slightly cheaper, which is kind of nice I suppose. (Unless you work for a large Wall Street firm who's revenue depends on retail investors paying high margins. But in that case my sympathy is quite limited.)
Concretely speaking, HFTs price discriminate when providing liquidity. Grandma gets a good price to sell her 2 lots of GOOG, but Bill Ackman and George Soros need to pay more to sell 20000 lots.
The same problems will not be necessarily manifested if the law is applied in the US, especially if Canada has similar laws. However, the points of the first link seem to hold.
The fact that one can shift trading in cross listed symbols to other venues doesn't mean that supply&demand also doesn't reduce market making (thereby increasing costs). In fact, Bernie Sanders explicitly hopes the tax will do exactly that.