I personally think the best way to rank posts is by simple activity myself, the system that DeviantArt uses, a simple recursive algorithm where the top post is the one that had a reply in one of it's children of the same level twice, but the tree is maintained.

So say we have a these posts:

    A
    - B
    - C
    - - D
    E
    - F
    - - G
    - H

Say that a new post, I, be made, which is a reply to H, then after that the tree would appear so:

    E
    - H
    - - I
    - F
    - - G
    A
    - B
    - C
    - - D

By replying to H, I has now pushed H to be the top child of E, and also pushed E above A.

This results into posts whose children have the most activity statistically are more visible, but if an inactive post be replied to, it will briefly be at the top and more visible, and any new post will also start at the top.

Essentially, it is the treed evolution of the traditional linear thread system where threads are simply ranked based on most recent replied. DeviantArt uses this system and it's boards do not feel as though they be an echo-chamber and are full of people challenging each other's views and trees seem to be more balanced out rather than al replies being under the top post, which became the most visible due to upvotes such that others are ignored completely.

This seems identical to futaba/chan-style "bumping" which is imo easily gamed without having some other variable (logarithmic time fall off or something) AND (has significant spam protection OR has significant moderation/user reporting system). It is usually paired with a post limit as well, so that eventually old conversations fall off and disappear and/or get archived.

Most traditional forums never had a timer system, and it did not seem to be needed.

It indeed resulted in some threads being alive for months, but that was only because the discussion in it was healthy and interesting, and new input on the same subject continued to be had.

They typically also do not have an archival system and often præfer that one revive an old thread that was dead for years rather than make a new one on the same subject, as in doing so all the old content becomes visible again for a fresh perspective.

I agree that often it is quite interesting to receive new replies with new input to a thread that died off three years ago.

I am not seeing these fora being gamed at all: in order to game them, one must provide content interesting enough to draw replies. — Visibility is purely a function of the number of replies, not of agreement.

I like the simplicity of it, but it could very easily be a victim of "forum sliding", where new posts are made with the purpose of moving undesirable topics out of sight.

It's possible, but they would be spam and dealt with, and I do not see this problem on DeviantArt at all.

You could use the API to get historical posts and comments and run the numbers to get a taste of the outcome instead of testing on the live site.

That feels like it would just turn into some type of toxic popularity contest where prominent posters that get a lot of engagement get boosted to the top, irregardless of the actual quality of said engagement. In addition it may also create some type of gatekeeping effect, though in my opinion that's not exactly a bad thing for niche communities such as this.