The new system Mr Johnson favours is known as Alternative Vote Plus and was first suggested by the Independent Commission on Electoral Reform, led by Lord Jenkins, in 1998.Well it's not that simple. What follows is (grossly) over-simplified.
Under AV Plus, voters would have two ballot papers: one for their constituency representative and a second for their favoured political party.
Most seats in the Commons would be filled with locally elected MPs, but the remainder would be allocated by proportional representation according to the number of votes cast for each party.
Calling this an "elegant" option, Mr Johnson said: "This is a genuinely radical alternative that only Labour in government can facilitate."
First of all, you (we, they?) need to decide the overall number of MPs. There is a case for a reduction from the current number of 646 MPs; it would be much more difficult to argue for an increase. But let us settle for retaining the current number of 646, at least for the purposes of illustration.
Next, how many MPs should be voted in by individual constituencies and how many by the party list system? Too few list MPs (less than 100, 150?) and the exercise kind of loses its point; too many (more than 200, 250?) and the constituency MPs are swamped. Again, let us settle - for illustration purposes - on 150 list MPs against 400 (in round numbers) constituency MPs.
Oh dear, if we are to have only 400 constituency MPs, then we need a wholesale revision of constituency boundaries. (Dismissing a few MPs from Scotland, Wales and Northern Ireland would not be nearly enough to get down to 400.) I suppose that means bringing in the Electoral Commission to do the donkey work, which would take a year or two. And whatever they come up with is bound to be wildly controversial.
Oh, and by the way, are we content to retain for constituency MPs the current first-past-the-post arrangements? Or should we opt for a system of elimination whereby the voters indicate preferences and the lowest-scoring candidates are dismissed, with their votes redistributed to other candidates until somebody gets above the magic level of 50%?
As for the party list elections, are these based on relatively small groupings of constituencies, say a dozen or so? Or on big regions, as in next week's euro-elections? And are we content with the arrangements established for next week's euro elections, whereby the voter has to choose the party rather than the individual candidates on the lists, thus enabling the parties to dictate who is likely to elected by putting them at the top of the list. Thus if you happen to like candidate no 4 on such-and-such a party's list, then tough (unless of course the three candidates above No 4 are elected as well).
I suppose that Mr Johnson is entitled to call this an elegant option, although it seems a bit of a dog's breakfast to me. But that does not mean we should not embrace some version of proportional representation, as it cannot be more anomalous than the present system. But let us not pretend that moving from one system to the other would be straightforward.