I am part of the Swiss Alpine Club as well as a rowing club. In both, the same recurring discussion: we travel with groups of varying numbers (4-20), and often a car is used as its price is significantly lower than that of the train if it is sufficiently filled. These trips often imply quite some distance and thus quite some CO2 emission. Moreover, they are often synchronised with many other leisure events and thus contribute to, much hated, weekend traffic jams. I would love to make these trips with the train, but to convince others a more competitive price would help.
Obviously, it is challenging to make a special offer that is sufficiently fair to all passengers. However, solutions could exist. For example, the national organisation in charge (Swiss Rowing, Swiss Alpine Club, and many many others) could be delegated to emit tickets with a group discount for groups smaller than 10 persons for certain events or activities. Indeed, special discounts already exist for large events (e.g. I have benefited from a significant discount for the GP Bern), and they seem to have much success.