If you're thinking of casting your vote for London mayor as 1st preference Labour, 2nd preference Green, then it actually makes sense to swap these around. Here's why…
The way the votes are counted is this:
All the 1st pref votes are tallied up, and if there's an outright winner (one candidate with more than 50% of the vote), they win. The end. But…
If not, then the candidate with the least votes is elimated, and all ballot papers with that candidate as 1st preference are looked at to take their 2nd preference instead.
If one candidate now has more than 50% of the vote, they win. If not, the next weakest candidate is eliminated, and any 1st pref ballots for that candidate are looked at to take their 2nd pref instead (unless the 2nd pref has already been eliminated as well).
This continues until 1 candidate has >50% of the votes.

Ultimately, each voter only gets one vote (because if your 2nd pref is used then your 1st pref is discarded), BUT…

If your 1st prefernce gets discarded it, is still included in the published statistics. This is important.
Labour have a very good chance of winning the mayoral ballot, so are unlikely to be eliminated in these "rounds". So if you put them as your 1st pref, then your 2nd preference will never get looked at and will never show up in any statistics. Anywhere.
If you swap those preferences around and put Green 1st, then even if they get eliminated and your Labour vote is used instead, that discarded Green vote still gets published in the stats.
This support for the Greens is important. It helps them to build credibility, which gains them votes in council elections and other future elections. And it sends a message to the elected Mayor that you lean on the Green side of Labour, not the Tory side.
It does not increase the chances of "letting the Tories in".

Also remember that you get votes for the London Assembly. The orange ballot paper is a *proportional* ballot, so voting for the Green Party on this ballot paper is a GREAT thing to do.
The same logic applies to voting Lib Dem, although they have a lot less support in London, so perhaps less effective.

The current Green Party London Assembly members are highly effective and a powerful force in holding the Mayor to account. That orange ballot paper is powerful.
Unlike the General Election system, the London electoral system is good. Use it.

#LondonMayor #LondonMayor2021 #VoteGreen #VoteLabour #VoteLibDem
Sorry, slight correction here, there is actually only one round of elimination.

The principles all still stand though. https://twitter.com/joel_xo/status/1390021554180870149
The fact that the elimination all happens in one go actually makes the case stronger, as if Greens aren't in the top two then your 2nd preference gets instantly counted.

(If there were multiple rounds, your 2nd pref wouldn't be counted until Greens became the bottom candidate.)
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