This system is a reinvention of range voting.

Like taw says, for causally rational voters this procedure collapses into approval voting. (Though Warren D. Smith of the Center for Range Voting argues that range voting is still better. In computer simulations (technical report), under many conditions, voters who (causally irrationally) choose non-extreme scores collectively reduce aggregated Bayesian regret. Non-extreme scores may help voters simulate non-causal rationality by a "nursery effect".)

I've thought about another voting system that might not collapse. In this system, each voter has the same power as in approval voting. Each voter can choose their approvals themselves, if they have the resources to choose tactically good votes themselves. The system also has a "public voting tactician", which is to voting what a public defender is to legal defense. Voters can give their preferences to the public voting tactician in the form of a utility function, and the tactician finds an equilibrium approval voting strategy for all the voters given their preferences.

(The real reason I am interested in this system is that it might get around problems of incommensurability and scaling of utility functions while still using full utility information.)

The tactician should be chosen to minimize the advantage which voters or groups of voters can get by using any other procedure to choose their votes, or by reporting their preferences non-honestly.

Parts of this system which that description doesn't define are:

• What information does the tactician have? Does it have the preferences of the other voters? Does it have the votes of the voters who did not give preferences to the tactician? If yes, then this may not be a secret ballot, and non-public-tactician voting tactics may be at an unfair disadvantage, preventing competitive pressure to change the public tactician. If no, then where does its beliefs about other voters' votes come from?
• What kind of equilibrium? A voter only has a causal incentive to vote sincerely and admissibly (i.e. monotonic non-decreasing and non-constant in their preferences) when their vote can make a difference. What prevents "all the voters vote for a least collectively preferred candidate" from being an equilibrium, if, in this equilibrium, no voter has a causal incentive to change their vote? Are mixed strategies or uncertainty needed to define the equilibrium? I think the system reduces the voters' utility functions to simple preference orderings unless it models more than infinitesimal uncertainty about other voters' strategies.
• Will there be voters or groups of voters who can do better by using a non-deterministic method to choose their input to the voting system? If so, should the tactician sacrifice determinism?
• Is the best public voting tactician computationally intractable?