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Computation is not free!
The main reason that procedural fairness does not lead to fairness is that the cost of computation in a trial is substantial, and therefore if one party has a larger budget, they can purchase more computation (via law firms) and have a greater chance of success.
worst-case, average case, o-notation to analyze how success grows with budget (or mb, how budget grows with success, or with opponent budget)?
1) Each party proposes a budget for the trial. Let S = the smaller of the proposals. Let L = the larger of the proposals. The judge can reduce L (but not beneath S, nor beneath 1% of the amount at stake) if they feel that it is too large.
2) The party that proposed L is asked if they wish to subsidize the other party.
2a) If L chooses not to subsidize, then S becomes the trial's budget, and neither party may spend more than S on legal expenses relating to the trial, and the losing party must reimburse the legal expenses of the winning party up to Y (see below).
2b) If L chooses to subsidize, they set the budget at whatever amount they want, provided that amount is greater than S. Call the amount they choose L2. Both parties may spend up to L2, but not more, on legal expenses relating to the trial. The party that set L2 must prepay the other party for any legal expenses that the other party wishes to incur (up to L2) after the other party has already spent S. At the end of the trial, the losing party must reimburse the legal expenses of the winning party up to Y (see below).
3) If the party that proposed L has, or is supported by an entity of, greater net worth than the entity S or the entity supporting it, then Y = S. Otherwise (if the larger entity proposed the smaller budget), then Y = (1-Q)*S + Q*(min(L, 1% of net worth of smaller entity)), where Q = min(1, net worth(S or the entity supporting S)/net worth(L or the entity supporting L) - 1). E.g. if the larger entity is twice the size of the smaller, but the larger proposed the smaller budget, then the larger budget is chosen, except that the smaller entity can't force a budget larger than 1% of its net worth.
One difficulty is if one party is already more 'prepared' for the trial than the other. We wouldn't want a party to game the system by spending a ton of money on legal analysis before the beginning of the trial, in essence escaping the limits by prepaying. On the one hand, if one entity is facing a large number of similar trials from different counterparties (say, 1000 different counterparties), we wouldn't want them to have to spend 1000 x $X on legal analysis instead of simply $X.
I propose that the trial judge can order one side to pay the other side's legal expenses if they deem previous legal preparation to be relevant to the trial -- but with the proviso that one 'preparation dollar' can only force up to one additional dollar of supporting an opponent even over multiple trials, e.g. if one side spend $X on date D, then even if they are taken to trial by 1000 different counterparties, once they have paid a sum of $X to any combination of these counterparties to make up for the prepreparation on date D, they cannot be forced to pay more preparation money relating to their preparation on date D -- PROVIDED that any written (or permanent in any media) results of the legal preparation which have been retained are publicly released after this exhaustion (e.g. if the $X on date D led to a memo summarizing various legal possibilities, and if the entity still has a copy of this memo, then this memo must be publicly released in order for the $X to be exhausted).
note: after writing this i found that other people have thought of similar things (e.g. I've suggested before in other threads that legal fees should be contributed to a shared pool and divided equally between both parties, with some minimum contribution set based on income and net worth. This would allow a defendant who is decidedly in the right to survive an attack by a significantly larger plaintiff." -- https://news.ycombinator.com/item?id=7406124
