Pendulum damping device intended to be incorporated into a drivetrain of a vehicle, notably into a clutch, comprising: a. a support which is rotatable about an axis of rotation and in which is made an aperture defining two support runway tracks, b. a pendulum assembly comprising: i. two oscillating masses and ii.a single connecting member pairing the two oscillating masses with one another and defining two pendulum-assembly runway tracks, c. a first and a second rolling member (40a, 40b), each of which defines a rolling surface designed for rolling on one, respectively the other, of the two support runway tracks and pendulum-assembly runway tracks so as to guide the oscillation of the pendulum assembly with respect to the support, the first and the second rolling members (40a, 40b) rolling along each runway track (41, 42) around a rest position on said track, wherein the single connecting member extends circumferentially between a first end and a second end and comprises a first zone, extending circumferentially between the first end and the rest position of the first rolling member, a second zone, extending circumferentially between the rest position of the second rolling member and the second end, and a third zone, extending circumferentially between the first zone and the second zone, characterized in that the single connecting member is riveted, the first zone and the second zone each comprising N first rivets each having a first diameter, N being a non-zero natural integer, and the third zone comprising R second rivets each having a second diameter, R being a natural integer, and in that the sum of the first diameters of the N first rivets of the first zone or of the second zone is strictly greater than the sum of the second diameters of the R second rivets of the third zone. a. a support which is rotatable about an axis of rotation and in which is made an aperture defining two support runway tracks, b. a pendulum assembly comprising: i. two oscillating masses and ii.a single connecting member pairing the two oscillating masses with one another and defining two pendulum-assembly runway tracks, i. two oscillating masses and ii.a single connecting member pairing the two oscillating masses with one another and defining two pendulum-assembly runway tracks, c. a first and a second rolling member (40a, 40b), each of which defines a rolling surface designed for rolling on one, respectively the other, of the two support runway tracks and pendulum-assembly runway tracks so as to guide the oscillation of the pendulum assembly with respect to the support, the first and the second rolling members (40a, 40b) rolling along each runway track (41, 42) around a rest position on said track, wherein the single connecting member extends circumferentially between a first end and a second end and comprises a first zone, extending circumferentially between the first end and the rest position of the first rolling member, a second zone, extending circumferentially between the rest position of the second rolling member and the second end, and a third zone, extending circumferentially between the first zone and the second zone, characterized in that the single connecting member is riveted, the first zone and the second zone each comprising N first rivets each having a first diameter, N being a non-zero natural integer, and the third zone comprising R second rivets each having a second diameter, R being a natural integer, and in that the sum of the first diameters of the N first rivets of the first zone or of the second zone is strictly greater than the sum of the second diameters of the R second rivets of the third zone. wherein the single connecting member extends circumferentially between a first end and a second end and comprises a first zone, extending circumferentially between the first end and the rest position of the first rolling member, a second zone, extending circumferentially between the rest position of the second rolling member and the second end, and a third zone, extending circumferentially between the first zone and the second zone, characterized in that the single connecting member is riveted, the first zone and the second zone each comprising N first rivets each having a first diameter, N being a non-zero natural integer, and the third zone comprising R second rivets each having a second diameter, R being a natural integer, and in that the sum of the first diameters of the N first rivets of the first zone or of the second zone is strictly greater than the sum of the second diameters of the R second rivets of the third zone.