I am not saying something is not amiss, just not sure what it is tbh.
When an Administrator is in the leader pool it gives this:-
<UnitGlobalStats>
<UnitType>Administrator</UnitType>
<Stat>
<EffectType>AdministrationAwarded</EffectType>
<Target>
<TargetType>Faction</TargetType>
</Target>
<BonusType>Flat</BonusType>
<Value>1</Value>
</Stat>
</UnitGlobalStats>
You also gain 4 from the hireing of an Administrator as this code shows:-
<UnitSpecialization>
<InternalName>Unit_Administrator</InternalName>
<DisplayName>Unit_Administrator_Name</DisplayName>
<Description>Unit_Administrator_Dec</Description>
<GlobalType>Administrator</GlobalType>
<GlobalCapAmount>10</GlobalCapAmount>
<Icon>Citizen_Administrator.png</Icon>
<Image>Crusade_Administrator.png</Image>
<Background>Citizen_BG_Admiral.png</Background>
<SelectSFX>UI/CITIZENS/ADMINISTRATOR_SELECT</SelectSFX>
<ImprovementType>AllImprovements</ImprovementType>
<CanTravel>false</CanTravel>
<Triggers>
<OnEvent>OnUnitGenerated</OnEvent>
<PerformAction>
<Action>AwardSpecificResource</Action>
<ValueParam>4</ValueParam>
<StringParam>Administration</StringParam>
</PerformAction>
</Triggers>
</UnitSpecialization>
When you then promote said Admin, you lose 1 Admin due to removing the Administrator from the Global Pool, then gain 5 more from the Promotion seen in this bit of code:-
<UnitSpecialization>
<InternalName>Promotion_Minister</InternalName>
<DisplayName>Promotion_Minister_Name</DisplayName>
<Description>Promotion_Minister_Dec</Description>
<GlobalType>Minister</GlobalType>
<Icon>GC3_Build_Starbases_Icon.png</Icon>
<Image>Crusade_Administrator.png</Image>
<Background>Citizen_BG_Admiral.png</Background>
<SelectSFX>UI/CITIZENS/ADMINISTRATOR_SELECT</SelectSFX>
<ImprovementType>AllImprovements</ImprovementType>
<CanTravel>false</CanTravel>
<Cost>
<EffectType>PromethionCost</EffectType>
<Target>
<TargetType>Faction</TargetType>
</Target>
<BonusType>OneTime</BonusType>
<Value>10</Value>
</Cost>
<Cost>
<EffectType>EpimetheusPollenCost</EffectType>
<Target>
<TargetType>Faction</TargetType>
</Target>
<BonusType>OneTime</BonusType>
<Value>1</Value>
</Cost>
<Triggers>
<OnEvent>OnUnitGenerated</OnEvent>
<PerformAction>
<Action>AwardSpecificResource</Action>
<ValueParam>5</ValueParam>
<StringParam>Administration</StringParam>
</PerformAction>
<DescriptionText>Promotion_Minister_ActionTriggerDec_0</DescriptionText>
</Triggers>
<Triggers>
<OnEvent>OnUnitGenerated</OnEvent>
<PerformAction>
<Action>KillUnitSelf</Action>
</PerformAction>
<DescriptionText>Promotion_Minister_ActionTriggerDec_1</DescriptionText>
</Triggers>
<Prerequ>
<UnitTypeFrom>Administrator</UnitTypeFrom>
</Prerequ>
</UnitSpecialization>
In total you gain 9 Admins per Promoted Administrator. if you pay attention to the tooltips you should in effect gain a total of 10, 5 from the Hireing :-
<String>Administrators provide 5 points for administration which in turn are consumed by Survey Ships, Colonies, and Starbases.</String>
And another 5 from the Promotion:-
<String>[ICON=Stat_Admin_Icon] Provides 5 more administrative resources. </String>
So yeah, either the Tooltip is wrong, or we are not getting what we should 