Return to Answer

private readonly Tuple<bool, Action>[] action;

// in constructor:
actions = new Tuple<bool, Action>[]
{
    Tuple.Create(settings.StopOnBackupCurrentInstallerFailure, DoBackupCurrentVersion),
    Tuple.Create(settings.StopOnUpdateCodeBaseFailure, DoGetLatestVersion),
    Tuple.Create(settings.StopOnCompileFailure, DoCompileCodeBase),
    Tuple.Create(settings.StopOnBuildInstallerFailure, DoBuildInstaller)
}

private bool ExecuteInternal()
{
    var errors = new List<string>();
    var logger = _logProvider.GetLogger(GetType().Name);
    var settings = Properties.Settings.Default;

    DoArchiveOldInstallers();

    foreach (var action in actions)
    {
        if (action.Item1 && !action.Item2())
            return false;
    }

    return true;
}

private readonly Tuple<bool, Func<bool>>[] action;

// in constructor:
actions = new Tuple<bool, Func<bool>>[]
{
    new Tuple<bool, Func<bool>>(settings.StopOnBackupCurrentInstallerFailure, DoBackupCurrentVersion),
    new Tuple<bool, Func<bool>>(settings.StopOnUpdateCodeBaseFailure, DoGetLatestVersion),
    new Tuple<bool, Func<bool>>(settings.StopOnCompileFailure, DoCompileCodeBase),
    new Tuple<bool, Func<bool>>(settings.StopOnBuildInstallerFailure, DoBuildInstaller)
}

private bool ExecuteInternal()
{
    var errors = new List<string>();
    var logger = _logProvider.GetLogger(GetType().Name);
    var settings = Properties.Settings.Default;

    DoArchiveOldInstallers();

    foreach (var action in actions)
    {
        if (action.Item1 && !action.Item2())
            return false;
    }

    return true;
}

The syntax to initialize the list of Tuples is not great. You could improve that by having a special type TupleList<T1, T2> : List<Tuple<T1, T2>>, which would have a method like void Add(T1 item1, T2 item2). That way, the initialization simplifies to:

actions = new TupleList<bool, Func<bool>>
{
    { settings.StopOnBackupCurrentInstallerFailure, DoBackupCurrentVersion },
    { settings.StopOnUpdateCodeBaseFailure, DoGetLatestVersion },
    { settings.StopOnCompileFailure, DoCompileCodeBase },
    { settings.StopOnBuildInstallerFailure, DoBuildInstaller }
}

But I'm not sure doing that would be worth it in this case.

And each action would be responsible for checking the right setting, if appropriate. (Actions that don't do any checks, like DoArchiveOldInstallers could be represented by a different type that inherits from the same base, or something like that.) But I'm not sure doing that would be worth it in this case.