A restricted multiple generator approach to enumerate personal support networks: An alternative to global important matters and satisficing in web surveys

•Satisficing occurs when the important matters (IM) generator is presented alone with one name box.•Five name boxes with IM alone elicit a more complete network with less measurement error.•The use of five topic-specific IM generators that record up to one alter per generator (R5D) is explored.•R5D is more aligned with the theoretical construct of the personal support (core) network.•R5D enumerates more cross-cutting, less diverse alters with less slippage in importance.