Q9: Did you ever consider a non-transitive preferential delegation model instead of the transitive delegations used by LiquidFeedback?
The proof on negative voting weight given in Issue #3 of “The Liquid Democracy Journal” [PD] seems to only cover hybrid models (i.e. transitive preferential delegations), as Figure 4.3 shows transitivity.
We never considered a preferential-only (i.e. non-transitive preferential) delegation model due to the considerations elaborated on in section 2.4.2 of our book, “The Principles of LiquidFeedback”. [PLF] Nonetheless, our proof [PD] given in Issue #3 also covers the case of non-transitive delegation systems. Non-transitive delegation systems would violate property 6 (“Equality of direct and delegating voters”). Figure 4.3, where transitive propagation is visible, is justified by the previous case 3 as well as property 6. Note, however, that property 6 does not demand transitivity. Properties 1 and 6 both explicitly make no statement on delegation chains:
Property 1: “[…] when one of A's delegates is delegating further […], no assumptions are made at this point.”
Property 6: “[…] This rule only applies if the delegates whose votes are copied do not delegate futher. No assumptions are made otherwise (see also Property 1)”
Therefore, also preferential-only delegation systems (i.e. systems without transitive delegation) are covered by our proof and cannot fulfill the 7 properties demanded in [PD]. The consequences of our findings are summarized in [Circular].
Q10: Why do you implement delegations through a transfer of voting weight? Wouldn't it be better to let participants publish “vote recommendations” and require voters to copy each vote recommendation instead of giving a general power of attorney through delegation? This way, each participant would always have the same voting weight, which is more democratic than having people with different voting weight, isn't it?
Transferring voting weight has the same effect as automatically copying the ballot of your delegate. Refer to Figures 2.7 and 2.8 in [PLF]. Requiring participants to manually copy a vote recommendation instead of giving a power of attorney would disadvantage those people who have less time because their vote wouldn't be counted unless they copy a vote recommendation for each respective issue being debated in the system. Moreover, people with technical abilities could program bots and be counted nonetheless. Therefore, disabling automatic delegations would only affect those people who couldn't program or use bots. This would create an imbalance between the influence of technically skilled persons or well-organized groups and people who do not know how to program or how to use bots. These considerations were already elaborated on in our book, “The Principles of LiquidFeedback”, section 2.4.2 (“Delegations and ‘one man – one vote’”). [PLF]
Additionally, publishing preferential ballots before the respective poll is closed facilitates tactical maneuvers, which has been mathematically proven with the Gibbard-Satterthwaite Theorem in 1973/1975. [Gibbard] See also [GoD].