I came up with this lengthy analogy in an email exchange with @sophiehannahCB1 and I’ve decided to share here (which I hope she doesn’t mind) because (a) I quite like it and (b) it took a long time to type and god damn but I’m going to make the most of it. It’s regarding the no-to-AV canard that people whose first choice(s) are for dinky little parties get more votes/more bites of the cherry/whatever than those whose first choice is for one of the 2-3 still slugging it out at the end. “You guys only get one turn at voting,” the cry goes, “whereas those lunatics down in the lost-my-deposit reaches get three or four. It’s not fair!”

It’s also not true; and I think it’s clear if you look at it from a slightly different perspective.

Here’s our example. There are five voters, they’re in my home constituency of Eastbourne (figures from memory, marginal Lib Dem (45%) vs Tory (40%); Labour scores 10% and 5% other, so currently ~15% of voters have effectively no impact at all because what’s the use? The result wouldn’t change if they didn’t bother turning up). But here they’re voting by voice, in a room (everyone is; imagine 20,000 5-voter rooms and a group of impartial electoral officials overseeing). None of them will - or indeed, can - change their minds unless they have no choice in the matter, and they’ve all pre-selected their preferences. And none of them know, at all, what the overall count is at any point.

Voter A is an ardent Tory. His first pick is the Conservatives and he’s not even thinking about a second choice.

Voter B is an ardent Lib Dem. His first is the LDs, but like many Liberals he’d rather see Labour in than the Conservatives, so he’s got Labour down as a second choice, though he doubts it’ll come to that.

Voter C is an ardent Labour voter, and they’re his first choice. But he knows - it’s hard not to round here - that it’s nigh impossible that they’ll do well. And so his second choice is Lib Dem, for much the same reason as B.

Voter D is a leftie. His first choice is Green, because he’d like to see them get a chance, followed by the Socialist Party, Labour, and finally (like C) the Lib Dems.

Voter E is a rightie. He’d like to stop the wops at Calais, so he’s got UKIP as a first choice. His second through nth choices are a string of minor nutjob parties who’ll be eliminated before they’re even considered, but when it comes down to it, he’d rather have blue than yellow; Tory is his final pick.

Voting has gone on for a while and the tiddlers have fallen. We’ll ignore them for now. As we join proceedings, there are five parties in it: LD, Tory, Labour, Green and UKIP.

"Let’s hear your votes, please," shouts the moderator.

A: “Tory.”

B: “Lib Dem.”

C: “Labour”

D: “Green.”

E: “UKIP.”

The votes are tallied and the totals for Eastbourne so far are compared: Tory 40%, LD 45%, Lab 10%, Green 1.5%, UKIP 3.5%. No one has hit 50% yet, so it’s still all to play for. The Greens are current last-runners and eliminated. The moderator steps back into the room.

"Another round," he says. "Votes please!"

A: “Tory.”

B: “Lib Dem.”

C: “Labour”

D: “Green.”

"Sorry," says the moderator. "They’re not available any more."

"OK," says D. "Socialists?"

"No."

"Labour, then."

"OK."

E: “UKIP.”

Once again the votes are tallied and compared. All the ex-Greens across Eastbourne have switched to Labour (in our example). Tory 40%, LD 45%, Lab 11.5%, UKIP 3.5%. No one has hit 50% yet, so it’s still all to play for. UKIP are current last-runners and eliminated. The moderator steps back into the room.

"Another round, chaps," he says.

A: “Tory.”

B: “Lib Dem.”

C: “Labour”

D: “Labour.”

E: “UKIP.”

"Sorry," says the moderator. "They’ve gone too."

"Bugger," says E. "Bloody Bolsheviks. What about a succession of minor nutjob parties?"

"Also gone."

"Well, in that case put me down for the Tories then."

Once again the votes are tallied and compared. All the ex-UKIP across Eastbourne have switched to Conservative (in our example). Tory 43.5%, LD 45%, Lab 11.5%. No one has hit 50% yet, so it’s still all to play for. Labour are now our final last-runners and eliminated. The moderator steps back into the room.

"Last round, chaps," he says. "Nearly there."

A: “Tory.”

B: “Lib Dem.”

C: “Labour”

"Sorry," says the moderator. "Just two left now."

"Crap," says C. "OK, Lib Dems."

D: “Same for me, I guess. Lib Dems too.”

E: “Tory.”

The votes are tallied and compared a final time. All the ex-Labour across Eastbourne have gone with the LDs, giving the Lib Dems 56.5% to the Tory 43.5% and a win.

How many times did each voter get to have their say? 4 times each. Perfectly equal. The only difference between those voters was that some of them changed their minds as they couldn’t go for who they’d originally have liked. They all had the same amount of say, even if A and B didn’t get to swing to someone else. A and B were just as important because, without them, and without the other As and Bs in all those other rooms around town, their parties of choice would have been eliminated instead.

In reality, not everyone will make use of their second choices (they’re not mandatory) and some people’s votes will end up not counting at all for the final run-in (because all they selected were minor parties eliminated early on; not much different to what you can expect from your vote for one of those under the current system). In reality, I also suspect more first choices will be for the smaller parties people feel more affinity towards rather than the closest-fit big party that stands a chance of winning.

So there you go. Think of it as a multi round run-off where everyone has to pick their voting order ahead of time, without getting the choice to change their minds when they see which way the wind is blowing. If they were able to do that, then yes, the minor party voters would have more influence, because they could choose how they’d affect the result while counting was in progress. But they can’t; they, and everyone else, has to choose how they’ll hedge their bets beforehand. So everyone has the same say in things.