It visualizes the effective power groups of voters have in proportion to their percentage of the votes. So for most winner-takes-all systems (conventional voting systems) it is a step function; if you have 51% of the vote you have 100% of the power (blue line). Some voting systems try to ameliorate this by requiring a supermajority; e.g. to change the constitution you need 2/3rds of the votes. This slows down legislation and also doesn’t really change the problem of proportionality.
Our paper talks about non-deterministic voting systems, systems that incorporate an element of chance. The simplest version would be the “random ballot”; everyone sends in their ballot, then one is drawn at random. This system is perfectly proportional. A voting bloc with 49% of the votes is no longer in power 0% of the time, but is now in power 49% of the time (green line).
Of course not all non-deterministic voting systems are as proportional as the random ballot. For example, say that instead of picking one ballot at random, we keep drawing ballots at random until we have two that pick the same candidate. Now you get something in between the random ballot and a conventional voting systems (red line).
There are an infinite amount of non-deterministic voting systems so these are just two simple examples and are not the actual non-deterministic voting systems we endorse. For a more sophisticated non-deterministic voting system you can take a look at MaxParC.
Also, as you may have noticed, EAs are mostly focused on individualistic interventions and are not that interested in this kind of systemic change (I don’t bother with my papers on this forum). If you want to discuss these types of ideas you might have more luck on the voting subreddit, the voting theory forum, or the electo wiki.
First of all, thanks for the suggestion. I will post this in the “Voting Theory Forum” (for papers I am also a participant in the “Decision Theory Forum”), and probably in electo wiki (the reddit looks too entropic).
I will read your paper and contact (by mail) you and Dr. Heitzig, including the gated version of my paper and some additional material and probably I will consult you on my next steps.
In any case, as commented before, in my view there is a massive difference between static voting and dynamic voting. With a single vote, Arrow is inevitable. When you vote many times in the i.i.d framework, you can communicate preference intensities, and the Arrow problem can be addressed. Unfortunately, when decisions interact, policy coordination by simple (sequential) voting looks intractable to me.
Hi Arturo,
You might be interested in this graph, from me and Jobst’s paper: “Should we vote in non-deterministic elections?”
It visualizes the effective power groups of voters have in proportion to their percentage of the votes. So for most winner-takes-all systems (conventional voting systems) it is a step function; if you have 51% of the vote you have 100% of the power (blue line).
Some voting systems try to ameliorate this by requiring a supermajority; e.g. to change the constitution you need 2/3rds of the votes. This slows down legislation and also doesn’t really change the problem of proportionality.
Our paper talks about non-deterministic voting systems, systems that incorporate an element of chance. The simplest version would be the “random ballot”; everyone sends in their ballot, then one is drawn at random. This system is perfectly proportional. A voting bloc with 49% of the votes is no longer in power 0% of the time, but is now in power 49% of the time (green line).
Of course not all non-deterministic voting systems are as proportional as the random ballot. For example, say that instead of picking one ballot at random, we keep drawing ballots at random until we have two that pick the same candidate. Now you get something in between the random ballot and a conventional voting systems (red line).
There are an infinite amount of non-deterministic voting systems so these are just two simple examples and are not the actual non-deterministic voting systems we endorse. For a more sophisticated non-deterministic voting system you can take a look at MaxParC.
Also, as you may have noticed, EAs are mostly focused on individualistic interventions and are not that interested in this kind of systemic change (I don’t bother with my papers on this forum). If you want to discuss these types of ideas you might have more luck on the voting subreddit, the voting theory forum, or the electo wiki.
First of all, thanks for the suggestion. I will post this in the “Voting Theory Forum” (for papers I am also a participant in the “Decision Theory Forum”), and probably in electo wiki (the reddit looks too entropic).
I will read your paper and contact (by mail) you and Dr. Heitzig, including the gated version of my paper and some additional material and probably I will consult you on my next steps.
In any case, as commented before, in my view there is a massive difference between static voting and dynamic voting. With a single vote, Arrow is inevitable. When you vote many times in the i.i.d framework, you can communicate preference intensities, and the Arrow problem can be addressed. Unfortunately, when decisions interact, policy coordination by simple (sequential) voting looks intractable to me.
Thank you very much for your comment,
Arturo