As per Augur guide page:

If holders fail to report accurately on the outcome of an event, or attempt to be dishonest – the Augur system redistributes the bad reporters Reputation to those who have reported accurately during the same reporting cycle.

How Augur system determines when to redistribute reputation tokens from the bad reporters? Is there any specific threshold?

The reporting system has undergone a major refactoring and so redistribution works somewhat differently now.

Reporting is now essentially a series of increasing stake on assertions that an outcome is correct. The first such staking of REP is the initial report, which is done by the designated reporter or whoever shows up if the designated reporter doesn't show.

Once an initial report is placed reporters may contribute to a dispute of the tentative outcome by asserting a different outcome. If they reach the dispute threshold the outcome they've asserted will become the new tentative winning outcome and there will be another window for reporters to dispute further. This process continues until a window passes with no dispute or until a fork occurs (once a dispute threshold is reached which accounts for 2.5% of the total REP supply).

The actual threshold for each dispute to be reached is provided by this formula:

2 * [ALL STAKE IN MARKET] - 3 * [STAKE ON ASSERTED OUTCOME]

This amount ensures that once a market is finalized the liquidated losing REP will provide a 50% ROI for the REP staked on the winning outcome.

So for example lets say the designated reporter shows up, and the required stake for them is 1 REP. They do the initial report and assert that outcome A is correct.

Once the fee window for the market begins reporters X and Y each contribute 1 REP to outcome B. Since the bond size for outcome B is 2 * 1 - 3 * 0 == 2 the dispute succeeds and the market's new tentative outcome is B.

If the market resolves here they will each receive their share of the 1 REP initially staked, thus giving them 1.5 REP total for their 1 REP stake.

If instead reporter Z stakes 3 REP on outcome A in the next fee window that bond will succeed since 2 * 3 - 3 * 1 == 3. In the event the market finalizes with outcome A now reporters X and Y will have their REP liquidated to pay the initial reporter and reporter Z. The initial reporter will get paid 1.5 REP and reporter Z gets 4.5.

FYI: That page is a bit out of date.

When reporters report on a market, they stake REP on their report. The reporter can choose how much they want to stake on any given report and there is no meaningful minimum (1 attorep). Eventually, the market will finalize with a final outcome. When this happens, anyone who staked on the final outcome will get a share of all REP staked on the market (both correct and incorrect) relative to their share relative to other reporters who staked on the final outcome.

As an example, if I stake 100 REP on outcome Apple and you stake 50 REP on outcome Apple and Cheater stakes 140 REP on outcome Banana and the final outcome is Apple, then I would get 290 * (100/150) and you would get 290 * (50/150) REP.

There are some caveats to the above explanation, but its "generally close enough to accurate". In reality, there are some other factors like anyone who correctly places a dispute bond (disputes an outcome and then further reporting proves that the dispute was a good call). In this case, the person who placed the dispute bond gets paid 2x their dispute bond input before reporters get any of the incorrect reporter REP (but correct reporters always get out at least as much as they staked). Also, if a fork occurs staked REP is automatically migrated to the branch for the outcome it was staked on, and there is no increase in REP other than dilution to the global REP pool due to incorrect REP going to other branches.

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