$\text{Votes}(\mathcal{B})$ Function
Votes Definition
For any votes $v$ and $v'$ , if $v$bal < $v'$ bal then $\lt$ $v'$LAMPORT, P. 6 — §2.1
This simple state that for any two unique votes, if the ballot id of one is less than the other then it is less than the other then the vote is less then that other one. This is just a formal way of saying that votes can be ordered by their ballot id
Votes Set
For any set $\mathcal{B}$ of ballots, the set $\text{Votes}(\mathcal{B})$ of votes in $\mathcal{B}$ was defined to consist of all votes $\text{v}$LAMPORT, P. 6 — §2.1
such that $\text{v}$pst $\in$ $\text{b}$vot, $\text{v}$bal = $B$bal , and $v$dec = $B$dec for some $B$ $\in$ $B$.
This defines a set of votes that exist within a given set of ballots. A vote is defined by three properties, the priest/node that cast it, the ballot id it is associated with and the decree/value it is voting for.
A formal definition might read.
A vote $v$ belongs to $\mathrm{Votes}(\mathcal{B})$ exactly when all of
the following hold for some $B \in \mathcal{B}$:
- $v.\mathrm{pst} \in B.\mathrm{vot}$
- $v.\mathrm{bal} = B.\mathrm{bal}$
- $v.\mathrm{dec} = B.\mathrm{dec}$