Product Owners definitely do not vote or otherwise influence the Team’s estimates during Planning Poker (unless they are also developer).

Basically, the best people to give estimates are the ones who will actually being doing the work.

The PO Fallacy

The PO Fallacy is that if the PO convince the team to give lower estimates then they can get more work done. They mean well as they are probably thinking about strategic goals, what their leaders wants or customer satisfaction. But the likely net result of compressing Story Point estimates is some or all of the following:

  • Overloaded Sprints
  • Not getting all of the Stories DONE that the Team committed to
  • Stories that do not meet the Team’s Definition of Done
  • Quality drops as Stories are rushed
  • Tech debt caused by the Team taking shortcuts to get everything completed
  • Unsustainable pace as the Team work evenings and weekends to complete the work they committed to
  • Unhappy developers
  • Staff turnover
  • Reduced velocity in the future as new team members are brought up to speed

How do PO influence estimates?

PO are often unaware of the effects of encouraging teams to compress their estimates. In this situation they might do the following:

  • Directly ask the Team to give a smaller number
  • Challenge the legitimacy of the estimation even though they lack the technical knowledge to do so
  • Challenge team members who give higher numbers during the initial rounds of estimation
  • Let the team know in advance what “has to be done”

Sometimes POs are aware that they shouldn’t be challenging the Team’s estimates so they use less direct methods.

  • Let a confederate in the team like a Scrum Master or a senior technical person know exactly what “has so be done” in the Sprint prior to the estimation session. The confederate then compresses the Team’s estimates on behalf of the PO
  • Give subconscious cues like laughing, making faces, rolling eyes when the team or a team member gives an estimate that they think is too high

What should the PO do during estimation?

Generally the safest approach is for the PO to stay silent and still and trust the team to come up with an accurate estimate.

More information https://www.infoq.com/news/2010/08/product-owner-planning-poker