MACI Tally Votes Circuit

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Parameters

#	Parameter	Description
0	State tree depth	Allows $(5^{n})$ signups.
1	State leaf batch depth	Allows $(5^{n})$ users' votes to be processed per batch.
2	Vote option tree depth	Allows $(5^{n})$ vote options.

info

A version working with non quadratic voting (non-qv) is also available. This version is called tallyVotesNonQv and is to be used when the Poll is not using the quadratic voting feature. Note that by default MACI works with quadratic voting.

Input signals

Input signal	Description
numSignUps	The number of users that signup
index	Start index of given batch
sbCommitment	Described below
currentTallyCommitment	Described below
newTallyCommitment	Described below
stateRoot	The root of the state tree after all messages have been applied
ballotRoot	The root of the ballot tree after all messages have been applied
sbSalt	The salt used to produce sbCommitment
ballots	The ballots in the batch being tallied
ballotPathElements	The Merkle path to each ballot leaf
votes	The votes in each ballot cast per result
currentResults	The current tally of votes per vote option
currentResultsRootSalt	A random value
currentSpentVoiceCreditSubtotal	The subtotal of voice credits spent across all vote options
currentSpentVoiceCreditSubtotalSalt	A random value
currentPerVOSpentVoiceCredits	The voice credits spent on each vote option so far
currentPerVOSpentVoiceCreditsRootSalt	A random value
newResultsRootSalt	A random value
newPerVOSpentVoiceCreditsRootSalt	A random value
newSpentVoiceCreditSubtotalSalt	A random value

sbCommitment

The commitment to stateRoot, ballotRoot, and sbSalt:

$poseidon_3([stateRoot, ballotRoot, sbSalt])$

Proving preimage of sbCommitment is one out of the several steps required to prove that the votes were tallied correctly. By establishing that the coordinator knows ballotRoot, the coordinator can (using other parts of the circuit) prove that they know the preimage of the ballot leaves in the batch being tallied.

currentTallyCommitment and newTallyCommitment

A tally is represented by a tally commitment, which is the $poseidon_3$ hash of:

1. $tc_r$: a commitment to the votes per option
   • This is the hash of the Merkle root $r_r$ of the votes and a salt $r_s$, computed as $poseidon_2([r_r, r_s])$
2. $tc_t$: a commitment to the total spent voice credits
   • This is the hash of the total spent voice credits $t_c$ and a salt $t_s$, computed as $poseidon_2([t_c, t_s])$
3. $tc_p$: a commitment to the spent voice credits per vote option
   • This is the hash of the Merkle root of the spent voice credits per vote option $p_v$ and a salt $p_s$, computed as $poseidon_2([p_v, p_s])$

The tally commitment is computed as such:

$poseidon_3([tc_r, tc_t, tc_p])$

Statements that the circuit proves

1. That the coordinator knows the preimage of sbCommitment
2. That index is less than or equal to numSignUps
3. That each ballot in ballots is in a member of the ballot tree with the Merkle root ballotRoot at indices batchStartIndex to batchStartIndex + (5 ** intStateTreeDepth)
4. That each set of votes (votes[i]) has the Merkle root $blt_r$ whose value equals ballots[i][1]
5. That the tally is valid, which is:
   • That the sum of votes per vote option is correct