They bet in the first quarter of fiscal year, then get paid off according to bet spread, except treasury throw in an extra 50 million. The spread will be bell shaped, and there will always be a broad spectrum of near winners who share the 50 million. Senators are free to work the spending to win the bet, senators do that anyway.
But, in the fixed point, the bet spread will represent reality, tail senators giving up and going for a bit more accuracy. The closer to zero the mean, the narrower the spread, then only the eccentric would exceed the implicit red/green. The spread gets narrower because the pricing orbits are shorter, each senator closely tracking the favorite programs through the maze.
They still have room to run the arbitrage moments, they just are more accurate about it. It is back to increasing the sample rate a bit for government on some programs, mark to market. Their queues have four or more, their arrivals very uncertain, bets difficult to rig. The senators will shorten things up for 50 mill in the old SE.
Let us sweeten the pot
The senators can vote their districts an aggregate fund, say 50 billion, used only for earmarks, if they need a name. The bets are paid such that every district is mostly an equal winner, except a small deviation to pay the senators their 50 million. The, in the aggregate, would vote higher and higher district earmarks and make more and more accurate budgets.
The senators would reach a point where the next step toward accuracy is a one time payment for their disappearance. They vote a trillion dollar earmark, each senator voting exactly the same deficit, and they cook the books, disband and do us all a favor.