I have build my helper for this case, it is mostly coming from this post

It is checked, not checked_value

Here is one I made for Bootstrap 4

  def multiselect_checkboxes(form, field, options, opts \\ []) do
    {selected, _} = get_selected_values(form, field, opts)
    selected_as_strings = Enum.map(selected, &"#{&1}")

    # Use inline mode by default
    class = opts[:class] || "form-check form-check-inline"
    # By default, input is active (not disabled)
    disabled = opts[:disabled]

    for {value, key} <- options, into: [] do
      id = input_id(form, field, key)
      content_tag(:div, class: class) do
        [
          tag(:input,
            name: input_name(form, field) <> "[]",
            id: id,
            class: "form-check-input",
            type: "checkbox",
            value: key,
            checked: Enum.member?(selected_as_strings, "#{key}"),
            disabled: disabled
          ),
          content_tag(:label, value, class: "form-check-label", for: id)
        ]
      end
    end
  end

  defp get_selected_values(form, field, opts) do
    {selected, opts} = Keyword.pop(opts, :selected)
    param = field_to_string(field)

    case form do
      %{params: %{^param => sent}} ->
        {sent, opts}

      _ ->
        {selected || input_value(form, field), opts}
    end
  end

  defp field_to_string(field) when is_atom(field), do: Atom.to_string(field)
  defp field_to_string(field) when is_binary(field), do: field

and I call it like this

  <label for="roles"><%= gettext("Roles") %></label>
  <div class="form-group">
    <%= 
      multiselect_checkboxes(
        f,
        :roles,
        select_roles(),
        selected: user_selected_roles(@changeset.data),
        disabled: is_self_and_last_admin?(
          @current_user, @changeset.data
        )
      )
    %>
  </div>

Some of the private functions are missing, but there are not difficult to reproduce.

There is nothing specific to Phoenix, I do remember having the same problem with Rails

Yes, it’s “value” if you use tag, “checked_value” if you use checkbox.