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A public ledger is antithetical to "high trust" anyway. A high trust society is one where you give hitchhikers rides without questioning too much about their motivations. If you have to do a criminal background check — which is just another form of consulting a public ledger of reputations — before letting him in your car, you are by definition not trusting him.
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Popularity and reputation are not the exact same thing. Reputation is about trust and predictability, while popularity is about awareness of the person and/or their reputation.

But your points largely stands. However, reputation is one of many tools that can be used to assess the worthiness of giving some work attention, but should be given a relatively low weight compared to other tools. Giving reputation a low, but non-zero weight allows bad actors to be rightfully put in their place and allows someone the ability and chance to "clean up" their reputation with effort.

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When I first considered this in the late 90's I was inspired by Google's Page Rank algorithm, and wanted something akin to that for humans in a social network.

My core idea (back in the early 00's when I cam up with it originally) was to identify a small cadre of trustworthy individuals in various sectors - lets say finance, computing, healthcare, etc (but more granular) and give them high trust (maybe a manual score of 10). Then let who they score, and who those people score "trickle down" as it does in Googles page rank. It was a variation on what Google later called trust rank, I suppose.

It would have either failed to launch completely or turned into a dystopian nightmare akin to China's Social Credit System. It may have even turned out worse than China's system because the goals of finance do not always align with the goals of humanity.

A more modern implementation could be built on the block chain and be made very profitable... while it crushes us all.

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