Every registered voter nominates one person to be their representative. Each representative requires exactly 9 nominations to be recognised as a representative.
Each rep then nominates one 2nd-level rep, each 2nd level rep requiring exactly 9 1st-level reps.
Each 2nd level rep nominates one 3rd
level rep, such that each 3rd level rep requires at least 9 2nd-level nominations.
And so on until there are about 9 cabinet members, who nominate one person to be the head of the government.
There are two issues that need to be addressed with this stupid idea. One is that the numbers won't all add up exactly, especially since some people won't engage with the system, and also that there won't be an exact multiple so there will be some people who can't get to nominate anyone. But I think this is OK.
I am thinking that we want multiples of 10 to give clarity as to the numbers of reps at every level, so I specified 9 nominations per rep. I am thinking that the prospective reps go around their contacts soliciting nominations, and individuals reply "yes I will be a nominator for you" or "no I can't because I have agreed to nominate my brother" or "no I can't because I am soliciting nominations myself".
Anyway after that first round, the Returning Officer checks that all the nominations are valid and that all Reps have the required 9 nominations with no duplicates etc. And then a list of the 1st level reps is published.
So for example take the UK which has 48,208,507 Registered Voters (as of July 4, 2024). Obviously not all voters can be bothered to engage with the system, but if they did, there would be 4,820,850 1st level reps nominated. At the very least there would be a couple of million or so 1st level reps.
I and 8 friends would nominate Arethusa, the leader of the philosophy group which we all go to in the local pub every other week. So Arethusa is now my 1st level rep.
Then we would move to the 2nd round of the process. The couple of million 1st level reps would each nominate another 1st level rep to be their 2nd level rep.
Arethusa could consult me and her other philosophy group friends if she wanted, or she could make her own nomination. She nominates Bernard, who lives next door to her, and who was soliciting nominations from the other people at that end of the street. So Bernard is now my 2nd level rep, alongside a few hundred thousand other 2nd level reps. Their nominations are checked and validated and a list of their names is published.
The 3rd round of the process continues as before. Bernard has to nominate one 2nd level rep; he nominates Cuthbert, the local retired GP who has been soliciting nominations from the affluent suburbs of the town. Again, Bernard would be advised to consult with Arethusa and the other 8 neighbours who had nominated him, and in turn she could well come to me and the other 8 pub philosophers who nominated her, and use our feedback to advise Bernard to help him decide whether to nominate Cuthbert or some other local worthy.
As before, nominations are validated, and a list of the tens of thousands of 3rd level reps is published.
The 4th round gets more interesting and there starts to be news coverage of how the thousands of 4th level reps are selected. Cuthbert feels the pressure of choosing from all of the tens of thousands of 3rd level reps, knowing that his choice will be on behalf of all the people below him in the nomination tree - 9 who nominated him (Bernard and 8 others), the 81 people who nominated him (Arthusa and 80 others), and the 729 people who nominated them (myself and 728 others.
Cuthbert decides that he is especially interested in health service reform, and so he joins with other retired GPs to nominate David, a retired consultant with an interest in this. However David only manages to find five other nominations, leaving him with six in total - not enough. Cuthbert has to make a snap decision - help David to find more nominations, or dump him and go and join another group of 3rd level reps. He sees that an ecological campaign group whose work he admires have 8 nominations for Deirdre, a distinguished botany professor, and so he decides to nominate her instead.
You see where this is going. Deirdre is validated as a 4th level rep alongside a few thousand others These people have real power in the system, since their job is to nominate the few hundred of 5th level reps, who will sit in the legislature and vote on laws and policy a bit like a parliamentary chamber in any other system.
Deirdre has complete freedom to decide which of the other 4th level reps she wants to nominate. She can consult back down the chain, as far as she wishes, or she can make her own decisions. In fact, she finds that there are quite a few other university professors who have been nominated as 4th level reps, and she starts contacting some of them to see if they might nominate her. She easily gets three people to agree, but she finds that there is also another emeritus professor of Physics, Donald, who is similarly soliciting university nominations, and who currently has five agreed nominees. They discuss within this group of 10 people, and though Donald has more, they all think that Deirdre may well be a better public speaker and so they all agree to nominate her. And so Deirdre is nominated as a 5th level rep and a Member of the Legislative Assembly. Her Department head gives her leave from her university duties so that she can take up her position as Nominated Representative in the National Parliament.
Once the parliament meets, its first item of business is to nominate a Cabinet of around 10 or so people. This 6th level process happens as before but for much higher stakes, with profiles of all the 5th level reps in the national newspapers, and daily reportage on who has been seen meeting whom, and with pundits speculating on the likely groupings within the parliament and possible cabinet nominees.
Anyway once the cabinet has been nominated, it meets, and then nominates the Prime Minister or Leader of the Government. This follows the same rules as before, requiring 9 nominees, with some highly technical legal qualifiers if there is an inconvenient number of Cabinet members (e.g. if there were only 9 cabinet members, then perhaps it would allow only 8 nominations for the 9th to be PM; or if there were 21 cabinet members and two contenders each got 9 nominations, there should be some system that was fair and transparent to select the PM).
Advantages of this system would be clear and direct chains of communication from every voter up to the top of the system, and a lessening of the ability of mass media and dirty money to pay to game the system. For example, I would know the direct chain from me to the government: Me, Arethusa, Bernard, Cuthbert, and then Deirdre is my representative in Parliament, and so on.
In this case I am lucky, because Deirdre is my 4th level rep as well as my parliamentary rep (5th level), meaning there are only 6 steps to the Leader of the Government instead of the maximum 7. Obviously some people will get much closer to power; Deirdre's postgraduate students who nominated her as their 1st level rep have a direct line to government.
You can also see that each Parliamentary rep has a whole network of clients they are accountable to, in a kind of nested heirarchical structure: Deirdre has the nine 4th level people who nominated her as Parliamentary rep; she has her own nine 3rd-level people including Cuthbert, and she also has 80 or so other 3rd-level people who nominated her nominators; then she has her own 9 2nd-level people, plus 700-ish other 2nd-level reps (including Bernard); and then she has her own 9 1st-level people, plus about six and a half thousand 1st level reps (including Arethusa). And finally she has her own ordinary voters (her 9 postgraduate students) plus something like 60,000 or so other ordinary voters including me. I am a bit hazy about these numbers.
Reps at every level would have clear authority and status within communities by virtue of being explicitly nominated by people. Local groups of reps would de fact have the authority to self-organise as local councils or run local government, though this could end up a little ad-hoc. I am not sure how the psychology of this process would play out, whether people would primarily nominate based on family or professional or local area connections. I think it would be quite hard to organise a political party under this system, because this system is built upon personal networks of trust and knowledge rather than abstract tribalism.