Numerical Unanimity
Anchors a unanimity regarding a numerical value
The proof of unanimity is a transaction on the blockchain, emitted if and only if all declared signatories have signed a value close enough to the average signed value.
Let
    n be the number of signatories
    a be the average signed value
    d be the percentage of deviation toward a
    S be the set of signed values.
The unanimity is reached if:
S=ns in S,(1d2)as(1+d2)a|S|=n \land \forall s \space in \space S, (1-\frac d 2)·a ≤ s ≤ (1+\frac d 2)·a
For example, say 2 signatories must sign a value with an authorized deviation of 2%. Unanimity is reached only in situation 2 below:
The unanimity logic is encoded by a smart contract that manages as many unanimity processes as necessary.
The contract admin address creates a specification for a consensus with:
    a unique consensus identifier
    the list of required signatories
A signatory signs with:
    the consensus id
    the value
A “unanimity” transaction is generated when all signatories haves signed a quasi-equal value.
Below is the archetype implementation:
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archetype unanimity
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variable admin : role = @tz1ZXf37ZNfVupt5GVyrPJ76q8kbjFuD2z7R
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asset sig identified by id signatory {
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id : string;
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signatory : address;
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value : int;
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}
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asset sig_spec {
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sid : string;
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signatories : list<address>;
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dev : int; /* deviation toward avg. in nb. of percent */
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expiration : date;
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signatures : partition<sig> = [];
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} with {
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s0 : 0 <= dev <= 100;
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}
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entry create_sig (i : string, s : list<address>, d : int) {
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called by admin
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effect {
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sig_spec.add({ sid = i; signatories = s; dev = d; expiration = (now + 1d) });
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}
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}
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function get_signatures(spid : string) : list<address * int> {
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var l : list<address * int> = [];
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for s in sig_spec[spid].signatures do
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l := prepend(l, (sig[s].signatory, sig[s].value));
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done;
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return l
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}
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function check_sig_data(spid : string) : bool {
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var avg = sig_spec[spid].signatures.sum(value) / sig_spec[spid].signatures.count();
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var min = (1 - sig_spec[spid].dev / 200) * avg;
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var max = (1 + sig_spec[spid].dev / 200) * avg;
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var check = true;
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for s in sig_spec[spid].signatures do
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check &= min <= sig[s].value <= max
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done;
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return check
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}
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entry unanimity (spid : string, l : list<address * int>, d : int) {
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called by selfaddress
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}
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entry failed (spid : string, l : list<address * int>, d : int) {
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called by selfaddress
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}
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entry sign (spid : string, v : int) {
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require {
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r0 : contains(sig_spec[spid].signatories, caller);
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}
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effect {
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sig_spec[spid].signatures.add({spid; caller; v });
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if sig_spec[spid].signatures.count() = length (sig_spec[spid].signatories) then (
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var sigs = get_signatures(spid);
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var d = sig_spec[spid].dev;
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var selfentry = if check_sig_data (spid) then self.unanimity else self.failed;
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transfer 0tz to entry selfentry((spid, sigs, d));
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sig_spec.remove(spid);
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);
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}
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}
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entry clear_expired () {
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called by admin
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effect {
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sig_spec.select(the.expiration < now).clear();
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}
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}
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