There is a good chance that  Issue 655880  will either fix this, or present an opportunity to fix this simultaneously.

 Issue 655000  has been merged into this issue.

 Issue 667255  has been merged into this issue.

 Issue 674248  has been merged into this issue.

This is an embarrassing bug that should be fixed at least in the next milestone.

I looked at this a little bit today. AFAICT, the problem is in PermissionSelectorRow::ChildPreferredSizeChanged [1], wherein we size the PermissionSelectorRow to its preferred size. Changing that method to simply call Layout() (and nothing else) seems to behave as expected, at least on Linux (haven't tested on Mac). The dropdowns do not jump around, and the entire bubble resizes if necessary to accommodate a long label. The parent()->SizeToPreferredSize() call seems to have been added a long time ago in [2] but is no longer necessary, I think, because WebsiteSettingsPopupView calls SizeToContents() when a permission setting changes, and it didn't back then when that call was added.

Intuitively it makes sense to me that we would want to simply do a fresh layout rather than forcing the row to its preferred size. We don't set the row to its preferred size otherwise, so I don't see why we should when a child view changes.

But, I don't really know much about Views yet so maybe this makes no sense. ¯\_(ツ)_/¯

[1] https://cs.chromium.org/chromium/src/chrome/browser/ui/views/website_settings/permission_selector_row.cc?dr=C&q=permissionselectorrow::child&sq=package:chromium&l=295

[2] https://chromium.googlesource.com/chromium/src/+/445e2128b7c28657b5ef4d268300734cb72d6d8d

https://codereview.chromium.org/2647633002/

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/f24aa8ad5db849c114c91cddcc297475b8ead2c8

commit f24aa8ad5db849c114c91cddcc297475b8ead2c8
Author: estark <estark@chromium.org>
Date: Fri Jan 20 08:45:41 2017

Do not size PermissionSelectorRow to preferred size

PermissionSelectorRow's preferred size is smaller than the width of the Page
Info Bubble, so when a permission changes, resizing to the preferred size means
that the row shrinks smaller than the other rows and the dropdown jumps around.

Instead, simply call Layout() to do a fresh layout of the row.

The parent()->SizeToPreferredSize() call is no longer necessary because
WebsiteSettingsPopupView calls SizeToContents() when a permission is
changed. Note that  bug 655880  may want to reintroduce the
PermissionSelectorRow::ChildPreferredSizeChanged override and propagate the
change to WebsiteSettingsPopupView that way instead of via OnPermissionChanged,
but it's not needed now -- and I'm guessing that, for that bug,
PermissionSelectorRow::ChildPreferredSizeChanged may want to call
parent()->PreferredSizeChanged(), rather than calling SizeToPreferredSize()
(which assumes that the parent ought to be at its preferred size).

BUG= 657286 
TEST=On Windows/Linux, visit https://google.com (or any other site) and open
Page Info by clicking on the security indicator in the omnibox. Change a
permission, change it again. Observe that the dropdown does not jump to the left
of where it started.

Review-Url: https://codereview.chromium.org/2647633002
Cr-Commit-Position: refs/heads/master@{#445017}

[modify] https://crrev.com/f24aa8ad5db849c114c91cddcc297475b8ead2c8/chrome/browser/ui/views/website_settings/permission_selector_row.cc

Requesting a merge for the commit in comment 12

Your change meets the bar and is auto-approved for M57. Please go ahead and merge the CL to branch 2987 manually. Please contact milestone owner if you have questions.
Owners: amineer@(clank), cmasso@(bling), ketakid@(cros), govind@(desktop)

For more details visit https://www.chromium.org/issue-tracking/autotriage - Your friendly Sheriffbot

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/85df4fc55cf9dd7200d6ef94914dd8c553e747bc

commit 85df4fc55cf9dd7200d6ef94914dd8c553e747bc
Author: Emily Stark <estark@google.com>
Date: Sat Jan 21 16:29:31 2017

Do not size PermissionSelectorRow to preferred size

PermissionSelectorRow's preferred size is smaller than the width of the Page
Info Bubble, so when a permission changes, resizing to the preferred size means
that the row shrinks smaller than the other rows and the dropdown jumps around.

Instead, simply call Layout() to do a fresh layout of the row.

The parent()->SizeToPreferredSize() call is no longer necessary because
WebsiteSettingsPopupView calls SizeToContents() when a permission is
changed. Note that  bug 655880  may want to reintroduce the
PermissionSelectorRow::ChildPreferredSizeChanged override and propagate the
change to WebsiteSettingsPopupView that way instead of via OnPermissionChanged,
but it's not needed now -- and I'm guessing that, for that bug,
PermissionSelectorRow::ChildPreferredSizeChanged may want to call
parent()->PreferredSizeChanged(), rather than calling SizeToPreferredSize()
(which assumes that the parent ought to be at its preferred size).

BUG= 657286 
TEST=On Windows/Linux, visit https://google.com (or any other site) and open
Page Info by clicking on the security indicator in the omnibox. Change a
permission, change it again. Observe that the dropdown does not jump to the left
of where it started.

Review-Url: https://codereview.chromium.org/2647633002
Cr-Commit-Position: refs/heads/master@{#445017}
(cherry picked from commit f24aa8ad5db849c114c91cddcc297475b8ead2c8)

Review-Url: https://codereview.chromium.org/2647173002 .
Cr-Commit-Position: refs/branch-heads/2987@{#11}
Cr-Branched-From: ad51088c0e8776e8dcd963dbe752c4035ba6dab6-refs/heads/master@{#444943}

[modify] https://crrev.com/85df4fc55cf9dd7200d6ef94914dd8c553e747bc/chrome/browser/ui/views/website_settings/permission_selector_row.cc

 Issue 657284  has been merged into this issue.