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Methodology for Applying the $ATONE Distribution as Detailed in Govgen Proposal 001

This page will describe the methodology to apply the $ATONE distribution detailed in GovGen proposal 001.

Note

While this documentation is related to Cosmos Hub proposal 848 and GovGen proposal 001, the code itself is supposed to be portable and reusable in other scenarios.

Get the Cosmos Hub Proposal 848 Snapshot Data

Create a directory data/prop848 and download the following files in that directory:

The way these files were extracted from Cosmos HUb proposal 848 snaphot is available here. If you prefer you can start from a Cosmos Hub node and extract all the data, everything is detailed here as already mentioned.

Verify Cosmos Hub Proposal 848 Tally

A good way to verify correctness of the data is to use it to compute the prop 848 tally and compare the results with the TallyResult field of the proposal object stored on-chain.

You can achieve this by running the following command:

$ go run . tally data/prop848/
173,165 votes
180 validators
1,061,423 delegations for 765,656 delegators
1,061,762 account balances
Computed total voting power 177,825,601,877,018
Yes percent: 0.517062127500689774
--- TALLY RESULT ---
+-----------+------------+------------+------------+------------+-------------+
|           |    YES     |     NO     | NOWITHVETO |  ABSTAIN   |    TOTAL    |
+-----------+------------+------------+------------+------------+-------------+
| computed  | 73,165,203 | 56,667,011 | 11,669,549 | 36,323,836 | 177,825,601 |
| from prop | 73,165,203 | 56,667,011 | 11,669,549 | 36,323,836 | 177,825,601 |
| diff      |          0 |          0 |          0 |          0 |           0 |
+-----------+------------+------------+------------+------------+-------------+

As printed in the output of the command, the diff is 0, meaning there is no difference between the tally computed from the data and the TallyResult field of the proposal.

Consolidate accounts

The program allows you to create a data/prop848/accounts.json file that consolidates all the relevant data for accounts. This file will be the starting point for the following steps, and will be fed to this very same program but using a different command.

$ go run . accounts data/prop848/
173,165 votes
180 validators
1,061,423 delegations for 765,656 delegators
1,061,762 account balances
1,948,588 accounts
data/prop848/accounts.json file created.

For example, here is the representation of an account in this file:

{
    "Address": "cosmos1zujjhe8j7fe0fzkxf4addzudx0s2j0zrwuyl2z",
    "Type": "/cosmos.auth.v1beta1.BaseAccount",
    "LiquidAmount": "155159.000000000000000000",
    "StakedAmount": "12404000.482447507703078623",
    "Vote": [
      {
        "option": 1,
        "weight": "1.000000000000000000"
      }
    ],
    "Delegations": [
      {
        "Amount": "12404000.481949488362528991",
        "ValidatorAddress": "cosmosvaloper130mdu9a0etmeuw52qfxk73pn0ga6gawkxsrlwf",
        "Vote": [
          {
            "option": 1,
            "weight": "1.000000000000000000"
          }
        ]
      },
      {
        "Amount": "0.000498019340549632",
        "ValidatorAddress": "cosmosvaloper16k579jk6yt2cwmqx9dz5xvq9fug2tekvlu9qdv",
        "Vote": [
          {
            "option": 1,
            "weight": "1.000000000000000000"
          }
        ]
      }
    ],
}

It gives access to the unbonded and bonded amounts (here liquid and staked amounts), the direct vote if present, the delegations and their relative vote.

Note

ModuleAccount and InterchainAccount are skipped.

Compute $ATONE distribution

Finally, let's compute the $ATONE distribution:

$ go run . distribution data/prop848/

The command above will output a table which provides an overview of the resulting distribution.

But more importantly, the command will create a file data/prop848/airdrop.json which for convenience you can find here already generated. The file lists all accounts and their relative proposed $ATONE balance.

The following table is also provided for a quick recap of the employed methodology:

DNV YES ABSTAIN NO NWV
Bonded multiplier C x malus 1 C 9 9 x bonus
Unbonded multiplier C x malus - - - -

A specific effort is made to ensure that non-voting categories (Did not Vote, Abstain and Not Staked (or Unbonded)) do not end up holding more than 1/3 of the supply. A tailored C multiplier is introduced to achieve this. See the following section for details on how this is achieved.

To obtain the final distribution, we also apply a decimation factor K = 0.1 when computing balances.

Important

The recap table above does not explicitly account for the K = 0.1 decimation factor. It is considered implicit as it will be applied indiscriminately alongside any other category-specific multiplier

According to the current calculations -- which may change -- the potential $ATONE distribution will be of around ~97 Millions.

TOTAL DID NOT VOTE YES NO NOWITHVETO ABSTAIN NOT STAKED
Distributed $ATONE 96,997,800 10,445,719 6,374,676 48,015,988 10,780,005 5,672,466 15,708,946
Percentage over total 11% 7% 50% 11% 6% 16%

As a comparison, here is the $ATOM distribution for prop848:

TOTAL DID NOT VOTE YES NO NOWITHVETO ABSTAIN NOT STAKED
Total $ATOM 342,834,268 66,855,758 70,428,501 55,519,213 11,664,818 35,679,919 102,686,059
Percentage over total 20% 21% 16% 3% 10% 30%

Multiplier Formula

This section details how the multiplier C for the non-voting $ATOM (Abstain, Did Not Vote, Not Staked) is calculated to result in them having less than or equal to 1/3 of the final $ATONE supply, or in general a fixed target percentage t.

Let's define the following variables:

  • C is the multiplier we want to compute to be applied to non-voting categories, i.e. Not Staked, Abstain and Did Not Vote

  • t the target relative percentage of $ATONE supply distributed to non-voting categories we want to achieve (known, 33%)

  • X is the supply in $ATOM (known)

  • Y is the supply in $ATONE

  • both X and Y will have an annotation indicating the portion of the supply:

    • Y voted Yes
    • A voted Abstain
    • N voted No
    • NWV voted No With Veto
    • DNV Did Not Vote
    • U Unbonded (Not Staked)

    For example, $X_{A}$ is the number of $ATOM that has voted ABSTAIN.

Using the above notation, we can express what we want to achieve mathemacally as:

$$\frac{Y_{A} + Y_{DNV} + Y_{U}}{Y_{A} + Y_{DNV} + Y_{U} + Y_{Y} + Y_{N} + Y_{NWV}} \leq t$$

It is know from the specifications of the distribution mechanism, disregarding any additional bonus or malus for simplicity and also because they are meant to be applied additionally to the C multiplier:

$$\left\{ \begin{aligned} & Y_{Y} = X_{Y} \\\ & Y_{N} = 9 \cdot X_{N} \\\ & Y_{NWV} = 9 \cdot X_{NWV} \\\ & Y_{A} + Y_{DNV} + Y_{U} = C \cdot X_{A} + C \cdot X_{DNV} + C \cdot X_{U} = C \cdot (X_{A} + X_{DNV} + X_{U}) \end{aligned} \right.$$

Which if plugged in the above equation gives:

$$\frac{C \cdot (X_{A} + X_{DNV} + X_{U})}{C \cdot (X_{A} + X_{DNV} + X_{U}) + X_{Y} + 9 \cdot X_{N} + 9 \cdot X_{NWV}} \leq t$$

Finally, let's isolate C:

$$\begin{align} C \cdot (X_{A} + X_{DNV} + X_{U}) &\leq t \cdot C \cdot (X_{A} + X_{DNV} + X_{U}) + t \cdot (X_{Y} + 9 \cdot X_{N} + 9 \cdot X_{NWV}) \\[10pt] (1 - t) \cdot C \cdot (X_{A} + X_{DNV} + X_{U}) &\leq t \cdot (X_{Y} + 9 \cdot X_{N} + 9 \cdot X_{NWV}) \\[10pt] C &\leq \frac{t}{1-t} \cdot \frac{(X_{Y} + 9 \cdot X_{N} + 9 \cdot X_{NWV})}{(X_{A} + X_{DNV} + X_{U})} \end{align}$$

Which gives the final formula described in the proposal 001.