# `Monty.Frameworks.Models.GraphMatching.MontyForGraphMatching`
[🔗](https://github.com/d-led/ex.tbp.monty/blob/v0.1.0/packages/ex_tbp_monty_core/lib/monty/frameworks/models/graph_matching/monty_for_graph_matching.ex#L1)

What the graph-matching model does rather than owns: the vote round.

Mirrors `tbp/monty/frameworks/models/graph_matching.py::MontyForGraphMatching`,
whose `_combine_votes` is the one piece of that class that is arithmetic rather
than message passing — this runtime does the message passing
(`Monty.Runtime.Step`), so the arithmetic is what is left to port.

## Two kinds of vote, and why this is the union

A module of this family names the objects it has **ruled out**
(`GraphLM.send_out_vote/1`), so what a receiver hears from several modules is
the union of what each ruled out: one module's doubt is not another's
confidence, and a sum of sets is not a thing.

The evidence family votes the other way round — it names the hypotheses it
still believes, with the pose and location each implies
(`MontyForEvidenceGraphMatching.combine_votes/2`) — and that is a different
calculation over a different shape. Monty's own `_combine_votes` branches on
exactly this (`isinstance(votes_per_lm[0], set)`), and so does
`Monty.Runtime.Step.State.combine_votes/2`: one model class drives both
families in Monty, and the shape of a vote is what tells it which calculation
to run.

## What a silent module contributes

Nothing. A module with no opinion — or one whose vote did not arrive before
the deadline — is `nil` in the reply map, and `nil` is not an empty set: the
empty set is a module that considered every object and ruled all of them in.
Union is the same either way, which is why this is a `reject` and not a
special case.

# `vote`

```elixir
@type vote() :: MapSet.t() | nil
```

A module's vote: the objects it has ruled out, or `nil` for silence.

# `combine_votes`

```elixir
@spec combine_votes(%{optional(term()) => vote()}, %{optional(term()) => [term()]}) ::
  %{
    optional(term()) => [term()]
  }
```

What each module hears, given every module's vote and the vote matrix.

Keyed by receiver, then a list of object names — the shape
`GraphLM.receive_votes/2` reads. A module the matrix gives no sources answers
`[]`, which is Monty's empty union.

---

*Consult [api-reference.md](api-reference.md) for complete listing*