The central idea is the possibility of shifting one’s own votes from one contest to another, of storing votes not spent on decisions that are low priorities for use on decisions that matter more.So there are a fixed set of proposals to vote on (let's say 10) and each senator gets 10 votes to divide between the proposals as she sees fit. The idea is that a minority will sometimes be able to push through a prized piece of legislation by saving up its votes from other contests.
The motivation seems reasonable (protecting minority interests and preventing deadlock) but I see a few problems with this:
Minority success as majority error: The majority have enough votes to stop everything the minority wants to do. Therefore, if the minority passes something that the majority doesn't want it is because the majority hasn't correctly calculated how many votes the minority would put on each proposal. To see this just imagine that the minority votes first: splitting their votes between the proposals according to their priorities. The best strategy for the majority (assuming they oppose the minority's goals) is to allocate just enough votes to beat each of the minority's totals. Therefore, if we don't see this it is the result of miscalculation by the majority in how they think the minority will act. The majority's actions won't reflect their priorities but what they perceive the priorities of the minority to be.
Agenda setting. A much bigger problem is the immense power that setting the agenda will have in these contests. In fact, if the minority has agenda power they may be able to push through any legislation they want. So let's go back to the example: 10 proposals and the minority gets to set the agenda. For instance, the president (D) making judicial nominations to a senate controlled by the opposite party (R). The senate is divided 55-45 against the president (hypothetical example- for now). So R have 550 votes and D 450. In normal circumstances R should succeed in blocking most, if not all of the president's nominees.
However, the president decides to nominate two utterly unacceptable nominees (-1000 payoff to R, +10 payoff to D): Ariana Huffington and Michael Moore, as well as eight normal candidates (-50 payoff to R, +50 payoff to D). D then announce that they randomly will put 275 votes on one of the two candidates (assume simultaneous voting for now). R now has the choice of how to respond. If they don't use all their votes against the two unacceptable candidates, they will be guaranteed a -1000 payoff compared to a -400 payoff if they let the other eight nominees past. So after the first two candidates are voted on, R have used all their votes up whilst D still have 175 votes remaining and can comfortably pass their eight candidates (+400).
The minority has essentially given itself complete power by having control over the agenda.
You might say that a party that did this would be punished by the voters. But that would assume that the public pay any attention to senate procedure.