I have an interesting solution to the non-anthropic problem. Firstly, the reward of 0 for voting differently is ignored in all the calculations, as it is assumed the other agent is acting identically. Therefore, its value is irrelevant (unless of course it becomes so high that the agents start deliberately employing randomisation in an attempt to try and vote differently, which would distort the problem).
However, consider what happens if you set the value to 9. In this case, you can forget about the other agent entirely. Voting heads if the coin was tails always loses exactly 1, while voting tails if the coin was heads loses 3. Since no method gives a probability higher than 3/4 for the coin being tails, the answer is simple: vote heads. Of course, this is a different problem, but it highlights the fact that any method which tells you to vote tails, and yet does not include the 0 anywhere in the calculations (since it assumes the agents can't possibly vote differently) is clearly suspect.
So you'd, for example, multiply by that zero.
A technical report of the Future of Humanity Institute (authored by me), on why anthropic probability isn't enough to reach decisions in anthropic situations. You also have to choose your decision theory, and take into account your altruism towards your copies. And these components can co-vary while leaving your ultimate decision the same - typically, EDT agents using SSA will reach the same decisions as CDT agents using SIA, and altruistic causal agents may decide the same way as selfish evidential agents.
Anthropics: why probability isn't enough
This paper argues that the current treatment of anthropic and self-locating problems over-emphasises the importance of anthropic probabilities, and ignores other relevant and important factors, such as whether the various copies of the agents in question consider that they are acting in a linked fashion and whether they are mutually altruistic towards each other. These issues, generally irrelevant for non-anthropic problems, come to the forefront in anthropic situations and are at least as important as the anthropic probabilities: indeed they can erase the difference between different theories of anthropic probability, or increase their divergence. These help to reinterpret the decisions, rather than probabilities, as the fundamental objects of interest in anthropic problems.