Put simply, participation aims at union with Christ. Pope Pius XII thought well of participation when it aligned with what was known and comfortable. Not exactly out at the margins, but affirming nonetheless:
106. These methods of participation in the Mass are to be approved and recommended when they are in complete agreement with the precepts of the Church and the rubrics of the liturgy. Their chief aim is to foster and promote the people’s piety and intimate union with Christ and His visible minister and to arouse those internal sentiments and dispositions which should make our hearts become like to that of the High Priest of the New Testament.
There seems to always be a “but” …
However, though they show also in an outward manner that the very nature of the sacrifice, as offered by the Mediator between God and (people),[Cf. 1 Tim. 2:5] must be regarded as the act of the whole Mystical Body of Christ, still they are by no means necessary to constitute it a public act or to give it a social character. And besides, a “dialogue” Mass of this kind cannot replace the high Mass, which, as a matter of fact, though it should be offered with only the sacred ministers present, possesses its own special dignity due to the impressive character of its ritual and the magnificence of its ceremonies. The splendor and grandeur of a high Mass, however, are very much increased if, as the Church desires, the people are present in great numbers and with devotion.
Curious that the externals of liturgy are praised here. But … the action, the activity remains that of Christ.
If you wish, consult Mediator Dei on the Vatican web site.
Catholic Sensibility 