"Calculated dimension" becomes unselectable/a measure?

[L_VN]

I have a case where we want to display certain dimensions based on measure criteria.

We have this backend:

Names:
load * inline [
	Name
    Alex
    Bo
    Casey
];

Facts:
load * inline [
	Measure, Factstype, Name
    1,	New York, Alex
    1, Los Angeles, Bo
    1, Los Angeles, Casey
];

Island:
load * inline [
	Show Dimension
    All
    Works in NY
    Works in LA
];

I have the values of Show Dimension in a filter pane, and only the Names that meet the criteria are shown according to this pick/match function:

=Pick(Match("Show Dimension", 'All', 'Works in NY', 'Works in LA'),
	Name
	,if(Aggr(Sum({<Factstype= {'New York'}>}Measure), Name)>0, Name)
	,if(Aggr(Sum({<Factstype= {'Los Angeles'}>}Measure), Name)>0, Name)
)

And this works, only the Names meet the criteria are shown. HOWEVER, they are not selectable (it is as if they are a measure and not a dimension.

If I reduce the pick/match to only take New York into account like this:

=Pick(Match("Show Dimension", 'All', 'Works in NY', 'Works in LA'),
	Name
	,if(Aggr(Sum({<Factstype= {'New York'}>}Measure), Name)>0, Name)
)

Then Bo and Casey are selectable, but Alex is not since he meets a criteria in the measure, even when 'All' is selected. 

The way I interpret it is that Qlik handles the Names whose expressions return a value as a measure and not a dimension. 

Is there a way around this?

[L_VN]

Show Dimension should have always one value selected

[Kushal_Chawda]

@L_VN  Just a little change in Island table

Island:
load * inline [
	Show Dimension, Dim
    All,1
    Works in NY,2
    Works in LA,3
];

You can use below calculated dimension

=pick(Dim,
Name,
aggr(Only({<Factstype= {'New York'}>}Name),Name),
aggr(Only({<Factstype= {'Los Angeles'}>}Name),Name)
)

[L_VN · Accepted solution]

The solution I found was to incapsulate the expression in another Aggr. This made it selectable. 

[L_VN]

The issue here is that in the real world example we have much more complex expressions that depend on an array of parameters, so implementing the solution only in back-end does not work.