For the avoidance of any doubt: don’t be a “hit and run entryist”, this post is not suggesting such a “scheme”. If you’re “indifferent or hostile to Labour Party politics” then I don’t really know why you’d want to be part of the selection, and don’t recommend you try and join as a member.
The post says “You can always cancel your membership (though of course I’d rather you’d stay a member).” That’s not advocating joining just to cancel—it’s saying you’re not bound in if you change your mind.
Forgive me, but your post didn’t exactly avoid any doubt, given:
1) The recommendation in the second paragraph is addressed to everyone regardless of political sympathy:
We believe that, if you’re a UK citizen or have lived in the UK for the last year, you should pay £4.38 to register to vote in the current Labour leadership, so you can help decide 1 of the 2 next candidates for Prime Minister. (My emphasis)
2) Your OP itself gives a few reasons for why those “indifferent or hostile to Labour Party politics” would want to be part of the selection. As you say:
For £4.38, you have a reasonable chance of determining the next candidate PM, and therefore having an impact in the order of billions of pounds. (Your emphasis)
Even a committed conservative should have preferences on “conditional on Labour winning in the next GE, which Labour MP would I prefer as PM?” (/plus the more Machiavellian “who is the candidate I’d most want leading Labour, given I want them to lose to the Conservatives?”).
3) Although the post doesn’t advocate joining just to cancel after voting, noting that one can ‘cancel any time’, alongside the main motivation being offered taking advantage of a time-limited opportunity for impact (and alongside the quoted cost being a single month of membership) makes this strategy not a dazzling feat of implicature (indeed, it would be the EV-maximising option taking the OP’s argument at face value).
Had the post merely used the oncoming selection in Labour to note there is an argument for political party participation similar to voting (i.e. getting a say in the handful of leading political figures); clearly stressed this applied across the political spectrum (and so was more a recommendation that EAs consider this reason to join the party they are politically sympathetic in expectation of voting in future leadership contests, rather than the one which happens to have a leadership contest on now); and strenuously disclaimed any suggestion of hit and run entryism (noting defection for various norms with existing members of the party, membership mechanisms being somewhat based on trust that folks aren’t going to ‘game them’, etc.), I would have no complaints. But it didn’t (although I hope it will), so here we are.
Have included a paragraph up at the top that hopefully adresses (some of?) your concerns. As it says in the paragraph, thanks for your comments!
“Edit: This argument applies across the political spectrum. One of the best arguments for political party participation is similar to voting i.e. getting a say in the handful of leading political figures. We recommend that effective altruists consider this as a reason to join the party they are politically sympathetic towards in expectation of voting in future leadership contests. We’re involved in the Labour Party—and Labour currently has a leadership election with only a week left to register to participate. So this post focuses on that as an example, and with a hope that if you’re Labour-sympathetic you consider registering to participate. We definitely do not suggest registering to participate if you’re not Labour-sympathetic. Don’t be a ‘hit and run entryist’ (Thanks Greg for the comments!).”
Thanks. I think it would be better, given you are recommending joining and remaining in the party, the ‘price’ isn’t quoted as a single month of membership.
One estimate could be the rate of leadership transitions. There have been ~17 in the last century of the Labour party (ignoring acting leaders). Rounding up, this gives an expected vote for every 5 years of membership, and so a price of ~£4.38*60 = ~£250 per leadership contest vote. This looks a much less attractive value proposition to me.
I actually thought the “of course I’d rather you’d stay a member” part was odd, since nowhere in the post up to that point had you said anything to indicate that you supported Labour yourself. The post doesn’t say anything about whether Labour itself is good or bad, or whether that should factor into your decision to join it at all, but in this comment it sounds like those are crucial questions for whether this step is right or not.