In the paper:
I suggest, as a useful mantra, Jeffrey’s (1983, 16) slogan “Choose for the person you expect to become once you have chosen.”
Whoa, no. That's a bad mantra. Wireheading, quantum immortality, doing meth - these are bad things.
The idea in the paper is is that you should decide by letting your "future selves" "vote," justified by the mantra above. And so their entire result is that in cases where your "future selves" who use different decision theories have different preference orderings, Arrow's theorem applies.
This not only requires you to throw away the cardinal information as gwern says, it only works if you make your decisions according to the mantra above! A reductio ad absurdum of this position would be that it can't even distinguish CDT from evil-CDT, which is where you always choose the locally worst option. Their result is really just the statement "some decision theories have different preference orderings," and should not be taken as a test of whether or not some decision theories are better than others.
Whoa, no. That's a bad mantra. Wireheading, quantum immortality, doing meth - these are bad things.
Briggs is here primarily considering cases where your preferences don't change as a result of your decision (but where your credences might). If we're interested in criticising the argument precisely as stated then perhaps this is a reasonable criticism but it's not an interesting criticism of Briggs' view which is to do with how we reason in cases where our decision gives us new information about the state of the world (ie. about changing credences not ch...
Briggs (2010) may be of interest to LWers. Opening: